@article{18585, abstract = {We present the census of Hβ+[OIII] 4960,5008 Åemitters at 6.87 galaxies. We report a rapid decline of the [OIII] luminosity density at z≳6−7 which cannot be explained by the evolution of the cosmic star-formation rate density. Finally we find that FRESCO detects in only 2h galaxies likely accounting for ∼10−20% of the ionising budget at z=7−8 (assuming an escape fraction of 10%), raising the prospect of directly detecting a significant fraction of the sources of reionisation with JWST.}, author = {Meyer, R. A. and Oesch, P. A. and Giovinazzo, E. and Weibel, A. and Brammer, G. and Matthee, Jorryt J and Naidu, R. P. and Bouwens, R. J. and Chisholm, J. and Covelo-Paz, A. and Fudamoto, Y. and Maseda, M. and Nelson, E. and Shivaei, I. and Xiao, M. and Herard-Demanche, T. and Illingworth, G. D. and Kerutt, J. and Kramarenko, Ivan and Labbe, I. and Leonova, E. and Magee, D. and Matharu, J. and Prieto Lyon, G. and Reddy, N. and Schaerer, D. and Shapley, A. and Stefanon, M. and Wozniak, M. A. and Wuyts, S.}, issn = {1365-2966}, journal = {Monthly Notices of the Royal Astronomical Society}, number = {1}, pages = {1067--1094}, publisher = {Oxford University Press}, title = {{JWST FRESCO: A comprehensive census of H β + [O iii] emitters at 6.8 < z < 9.0 in the GOODS fields}}, doi = {10.1093/mnras/stae2353}, volume = {535}, year = {2024}, } @article{18493, abstract = {Context. The escape of Lyman-α photons at redshifts greater than two is an ongoing subject of study and an important quantity to further understanding of Lyman-α emitters (LAEs), the transmission of Lyman-α photons through the interstellar medium and intergalactic medium, and the impact these LAEs have on cosmic reionisation. Aims. This study aims to assess the Lyman-α escape fraction, fesc, Lyα, over the redshift range 2.9 < z < 6.7, focusing on Very Large Telescope/Multi Unit Spectroscopic Explorer (VLT/MUSE) selected, gravitationally lensed, intrinsically faint LAEs. These galaxies are of particular interest as the potential drivers of cosmic reionisation. Methods. We assessed fesc, Lyα in two ways: through an individual study of 96 LAEs behind the A2744 lensing cluster, with James Webb Space Telescope/Near-Infrared Camera (JWST/NIRCam) and HST data, and through a study of the global evolution of fesc, Lyα using the state-of-the-art luminosity functions for LAEs and the UV-selected ‘parent’ population (dust-corrected). We compared these studies to those in the literature based on brighter samples. Results. We find a negligible redshift evolution of fesc, Lyα for our individual galaxies; it is likely that it was washed out by significant intrinsic scatter. We observed a more significant evolution towards higher escape fractions with decreasing UV magnitude and fit this relation. When comparing the two luminosity functions to derive fesc, Lyα in a global sense, we saw agreement with previous literature when integrating the luminosity functions to a bright limit. However, when integrating using a faint limit equivalent to the observational limits of our samples, we observed enhanced values of fesc, Lyα, particularly around z ∼ 6, where fesc, Lyα becomes consistent with 100% escape. This indicates for the faint regimes we sampled that galaxies towards reionisation tend to allow very large fractions of Lyman-α photons to escape. We interpret this as evidence of a lack of any significant dust in these populations; our sample is likely dominated by young, highly star-forming chemically unevolved galaxies. Finally, we assessed the contribution of the LAE population to reionisation using our latest values for fesc, Lyα and the LAE luminosity density. The dependence on the escape fraction of Lyman continuum photons is strong, but for values similar to those observed recently in z ∼ 3 LAEs and high-redshift analogues, LAEs could provide all the ionising emissivity necessary for reionisation.}, author = {Goovaerts, I. and Thai, T. T. and Pello, R. and Tuan-Anh, P. and Laporte, N. and Matthee, Jorryt J and Nanayakkara, T. and Pharo, J.}, issn = {1432-0746}, journal = {Astronomy & Astrophysics}, publisher = {EDP Sciences}, title = {{Charting the Lyman-α escape fraction in the range 2.9 < z < 6.7 and consequences for the LAE reionisation contribution}}, doi = {10.1051/0004-6361/202451432}, volume = {690}, year = {2024}, } @article{18523, abstract = {Recent observations from the EIGER JWST program have measured for the first time the quasar–galaxy cross-correlation function at z ≈ 6. The autocorrelation function of faint z ≈ 6 quasars was also recently estimated. These measurements provide key insights into the properties of quasars and galaxies at high redshift and their relation with the host dark matter haloes. In this work, we interpret these data building upon an empirical quasar population model that has been applied successfully to quasar clustering and demographic measurements at z ≈ 2–4. We use a new, large-volume N-body simulation with more than a trillion particles, FLAMINGO-10k, to model quasars and galaxies simultaneously. We successfully reproduce observations of z ≈ 6 quasars and galaxies (i.e. their clustering properties and luminosity functions), and infer key quantities such as their luminosity–halo mass relation, the mass function of their host haloes, and their duty cycle/occupation fraction. Our key findings are (i) quasars reside on average in ≈ 1012.5 M haloes (corresponding to ≈ 5σ fluctuations in the initial conditions of the linear density field), but the distribution of host halo masses is quite broad; (ii) the duty cycle of (UV-bright) quasar activity is relatively low (≈ 1 per cent); (iii) galaxies (that are bright in [O III]) live in much smaller haloes (≈ 1010.9 M) and have a larger duty cycle (occupation fraction) of ≈ 13 per cent. Finally, we focus on the inferred properties of quasars and present a homogeneous analysis of their evolution with redshift. The picture that emerges reveals a strong evolution of the host halo mass and duty cycle of quasars at z ≈ 2–6, and calls for new investigations of the role of quasar activity across cosmic time.}, author = {Pizzati, Elia and Hennawi, Joseph F. and Schaye, Joop and Schaller, Matthieu and Eilers, Anna Christina and Wang, Feige and Frenk, Carlos S. and Elbers, Willem and Helly, John C. and Mackenzie, Ruari and Matthee, Jorryt J and Bordoloi, Rongmon and Kashino, Daichi and Naidu, Rohan P. and Yue, Minghao}, issn = {1365-2966}, journal = {Monthly Notices of the Royal Astronomical Society}, number = {4}, pages = {3155--3175}, publisher = {Oxford University Press}, title = {{A unified model for the clustering of quasars and galaxies at z ≈ 6}}, doi = {10.1093/mnras/stae2307}, volume = {534}, year = {2024}, } @article{18527, abstract = {Context. Galaxies evolve through a dynamic exchange of material with their immediate surrounding environment, the so-called circumgalactic medium (CGM). Understanding the physics of gas flows and the nature of the CGM is fundamental to studying galaxy evolution, especially at 4 ≤ z ≤ 6 (i.e., after the Epoch of Reionization) when galaxies rapidly assembled their masses and reached their chemical maturity. Galactic outflows are predicted to enrich the CGM with metals, although it has also been suggested that gas stripping in systems undergoing a major merger may play a role. Aims. In this work, we explore the metal enrichment of the medium around merging galaxies at z ∼ 4.5, observed by the ALMA Large Program to INvestigate [CII] at Early times (ALPINE). To do so, we study the nature of the [CII] 158 μm emission in the CGM around these systems, using simulations to help disentangle the mechanisms contributing to the CGM metal pollution. Methods. By adopting an updated classification of major merger systems in the ALPINE survey, we selected and analyzed merging galaxies whose components can be spatially and/or spectrally resolved in a robust way. This makes it possible to distinguish between the [CII] emission coming from the single components of the system and that coming from the system as a whole. We also made use of the dustyGadget cosmological simulation to select synthetic analogs of observed galaxies and guide the interpretation of the observational results. Results. We find a large diffuse [CII] envelope (≳20 kpc) embedding all the merging systems, with at least 25% of the total [CII] emission coming from the medium between the galaxies. Using predictions from dustyGadget, we suggest that this emission has a multi-fold nature, with dynamical interactions between galaxies playing a major role in stripping the gas and enriching the medium with heavy elements.}, author = {Di Cesare, Claudia and Ginolfi, M. and Graziani, L. and Schneider, R. and Romano, M. and Popping, G.}, issn = {1432-0746}, journal = {Astronomy & Astrophysics}, publisher = {EDP Sciences}, title = {{Carbon envelopes around merging galaxies at z ~ 4.5}}, doi = {10.1051/0004-6361/202449164}, volume = {690}, year = {2024}, } @inproceedings{18890, abstract = {Deep Neural Collapse (DNC) refers to the surprisingly rigid structure of the data representations in the final layers of Deep Neural Networks (DNNs). Though the phenomenon has been measured in a variety of settings, its emergence is typically explained via data-agnostic approaches, such as the unconstrained features model. In this work, we introduce a data-dependent setting where DNC forms due to feature learning through the average gradient outer product (AGOP). The AGOP is defined with respect to a learned predictor and is equal to the uncentered covariance matrix of its input-output gradients averaged over the training dataset. The Deep Recursive Feature Machine (Deep RFM) is a method that constructs a neural network by iteratively mapping the data with the AGOP and applying an untrained random feature map. We demonstrate empirically that DNC occurs in Deep RFM across standard settings as a consequence of the projection with the AGOP matrix computed at each layer. Further, we theoretically explain DNC in Deep RFM in an asymptotic setting and as a result of kernel learning. We then provide evidence that this mechanism holds for neural networks more generally. In particular, we show that the right singular vectors and values of the weights can be responsible for the majority of within-class variability collapse for DNNs trained in the feature learning regime. As observed in recent work, this singular structure is highly correlated with that of the AGOP.}, author = {Beaglehole, Daniel and Súkeník, Peter and Mondelli, Marco and Belkin, Mikhail}, booktitle = {38th Annual Conference on Neural Information Processing Systems}, issn = {1049-5258}, location = {Vancouver, Canada}, publisher = {Neural Information Processing Systems Foundation}, title = {{Average gradient outer product as a mechanism for deep neural collapse}}, doi = {10.52202/079017-4156}, volume = {37}, year = {2024}, } @inproceedings{18875, abstract = {Current state-of-the-art methods for differentially private model training are based on matrix factorization techniques. However, these methods suffer from high computational overhead because they require numerically solving a demanding optimization problem to determine an approximately optimal factorization prior to the actual model training. In this work, we present a new matrix factorization approach, BSR, which overcomes this computational bottleneck. By exploiting properties of the standard matrix square root, BSR allows to efficiently handle also large-scale problems. For the key scenario of stochastic gradient descent with momentum and weight decay, we even derive analytical expressions for BSR that render the computational overhead negligible. We prove bounds on the approximation quality that hold both in the centralized and in the federated learning setting. Our numerical experiments demonstrate that models trained using BSR perform on par with the best existing methods, while completely avoiding their computational overhead.}, author = {Kalinin, Nikita and Lampert, Christoph}, booktitle = {38th Annual Conference on Neural Information Processing Systems}, issn = {1049-5258}, location = {Vancouver, Canada}, publisher = {Neural Information Processing Systems Foundation}, title = {{Banded square root matrix factorization for differentially private model training}}, doi = {10.52202/079017-0560}, volume = {37}, year = {2024}, } @article{18760, abstract = {With the remarkable sensitivity and resolution of JWST in the infrared, measuring rest-optical kinematics of galaxies at z > 5 has become possible for the first time. This study pilots a new method for measuring galaxy dynamics for highly multiplexed, unbiased samples by combining FRESCO NIRCam grism spectroscopy and JADES medium-band imaging. Here we present one of the first JWST kinematic measurements for a galaxy at z > 5. We find a significant velocity gradient, which, if interpreted as rotation, yields Vrot = 305 ± 70 km s−1, and we hence refer to this galaxy as Twister-z5. With a rest-frame optical effective radius of re = 2.25 kpc, the high rotation velocity in this galaxy is not due to a compact size, as may be expected in the early Universe, but rather to a high total mass, (math formula). This is a factor of roughly 10× higher than the stellar mass within re. We also observe that the radial Hα equivalent width profile and the specific star formation rate map from resolved stellar population modeling are centrally depressed by a factor of ∼1.5 from the center to re. Combined with the morphology of the line-emitting gas in comparison to the continuum, this centrally suppressed star formation is consistent with a star-forming disk surrounding a bulge growing inside out. While large, rapidly rotating disks are common to z ∼ 2, the existence of one after only 1 Gyr of cosmic time, shown for the first time in ionized gas, adds to the growing evidence that some galaxies matured earlier than expected in the history of the Universe.}, author = {Nelson, Erica and Brammer, Gabriel and Giménez-Arteaga, Clara and Oesch, Pascal A. and Naidu, Rohan P. and Übler, Hannah and Matharu, Jasleen and Shapley, Alice E. and Whitaker, Katherine E. and Wisnioski, Emily and Förster Schreiber, Natascha M. and Smit, Renske and Van Dokkum, Pieter and Chisholm, John and Endsley, Ryan and Hartley, Abigail I. and Gibson, Justus and Giovinazzo, Emma and Illingworth, Garth and Labbe, Ivo and Maseda, Michael V. and Matthee, Jorryt J and Covelo Paz, Alba and Price, Sedona H. and Reddy, Naveen A. and Shivaei, Irene and Weibel, Andrea and Wuyts, Stijn and Xiao, Mengyuan and Alberts, Stacey and Baker, William M. and Bunker, Andrew J. and Cameron, Alex J. and Charlot, Stephane and Eisenstein, Daniel J. and De Graaff, Anna and Ji, Zhiyuan and Johnson, Benjamin D. and Jones, Gareth C. and Maiolino, Roberto and Robertson, Brant and Sandles, Lester and Suess, Katherine A. and Tacchella, Sandro and Williams, Christina C. and Witstok, Joris}, issn = {2041-8213}, journal = {Astrophysical Journal Letters}, number = {2}, publisher = {IOP Publishing}, title = {{Ionized gas kinematics with FRESCO: An extended, massive, rapidly rotating galaxy at z = 5.4}}, doi = {10.3847/2041-8213/ad7b17}, volume = {976}, year = {2024}, } @article{18584, abstract = {In this paper, we describe the "Medium Bands, Mega Science" JWST Cycle 2 survey (JWST-GO-4111) and demonstrate the power of these data to reveal both the spatially integrated and spatially resolved properties of galaxies from the local Universe to the era of cosmic dawn. Executed in 2023 November, MegaScience obtained ∼30 arcmin2 of deep multiband NIRCam imaging centered on the z ∼ 0.3 A2744 cluster, including 11 medium-band filters and the two shortest-wavelength broadband filters, F070W and F090W. Together, MegaScience and the UNCOVER Cycle 1 treasury program provide a complete set of deep (∼28–30 magAB) images in all NIRCam medium- and broadband filters. This unique data set allows us to precisely constrain photometric redshifts, map stellar populations and dust attenuation for large samples of distant galaxies, and examine the connection between galaxy structures and formation histories. MegaScience also includes ∼17 arcmin2 of NIRISS parallel imaging in two broadband and four medium-band filters from 0.9 to 4.8 μm, expanding the footprint where robust spectral energy distribution (SED) fitting is possible. We provide example SEDs and multiband cutouts at a variety of redshifts, and use a catalog of JWST spectroscopic redshifts to show that MegaScience improves both the scatter and catastrophic outlier rate of photometric redshifts by factors of 2–3. Additionally, we demonstrate the spatially resolved science enabled by MegaScience by presenting maps of the [O iii] line emission and continuum emission in three spectroscopically confirmed z > 6 galaxies. We show that line emission in reionization-era galaxies can be clumpy, extended, and spatially offset from continuum emission, implying that galaxy assembly histories are complex even at these early epochs. We publicly release fully reduced mosaics and photometric catalogs for both the NIRCam primary and NIRISS parallel fields (jwst-uncover.github.io/megascience).}, author = {Suess, Katherine A. and Weaver, John R. and Price, Sedona H. and Pan, Richard and Wang, Bingjie and Bezanson, Rachel and Brammer, Gabriel and Cutler, Sam E. and Labbé, Ivo and Leja, Joel and Williams, Christina C. and Whitaker, Katherine E. and Atek, Hakim and Dayal, Pratika and De Graaff, Anna and Feldmann, Robert and Franx, Marijn and Fudamoto, Yoshinobu and Fujimoto, Seiji and Furtak, Lukas J. and Goulding, Andy D. and Greene, Jenny E. and Khullar, Gourav and Kokorev, Vasily and Kriek, Mariska and Lorenz, Brian and Marchesini, Danilo and Maseda, Michael V. and Matthee, Jorryt J and Miller, Tim B. and Mitsuhashi, Ikki and Mowla, Lamiya A. and Muzzin, Adam and Naidu, Rohan P. and Nanayakkara, Themiya and Nelson, Erica J. and Oesch, Pascal A. and Setton, David J. and Shipley, Heath and Smit, Renske and Spilker, Justin S. and Van Dokkum, Pieter and Zitrin, Adi}, issn = {1538-4357}, journal = {Astrophysical Journal}, number = {1}, publisher = {IOP Publishing}, title = {{Medium bands, mega science: A JWST/NIRCam medium-band imaging survey of A2744}}, doi = {10.3847/1538-4357/ad75fe}, volume = {976}, year = {2024}, } @inproceedings{18996, abstract = {We consider the linear causal representation learning setting where we observe a linear mixing of d unknown latent factors, which follow a linear structural causal model. Recent work has shown that it is possible to recover the latent factors as well as the underlying structural causal model over them, up to permutation and scaling, provided that we have at least d environments, each of which corresponds to perfect interventions on a single latent node (factor). After this powerful result, a key open problem faced by the community has been to relax these conditions: allow for coarser than perfect single-node interventions, and allow for fewer than d of them, since the number of latent factors d could be very large. In this work, we consider precisely such a setting, where we allow a smaller than d number of environments, and also allow for very coarse interventions that can very coarsely \textit{change the entire causal graph over the latent factors}. On the flip side, we relax what we wish to extract to simply the \textit{list of nodes that have shifted between one or more environments}. We provide a surprising identifiability result that it is indeed possible, under some very mild standard assumptions, to identify the set of shifted nodes. Our identifiability proof moreover is a constructive one: we explicitly provide necessary and sufficient conditions for a node to be a shifted node, and show that we can check these conditions given observed data. Our algorithm lends itself very naturally to the sample setting where instead of just interventional distributions, we are provided datasets of samples from each of these distributions. We corroborate our results on both synthetic experiments as well as an interesting psychometric dataset. The code can be found at https://github.com/TianyuCodings/iLCS.}, author = {Chen, Tianyu and Bello, Kevin and Locatello, Francesco and Aragam, Bryon and Ravikumar, Pradeep Kumar}, booktitle = {38th Conference on Neural Information Processing Systems}, issn = {1049-5258}, location = {Vancouver, Canada}, publisher = {Neural Information Processing Systems Foundation}, title = {{Identifying general mechanism shifts in linear causal representations}}, doi = {10.52202/079017-1343}, volume = {37}, year = {2024}, } @article{14451, abstract = {We investigate the potential of Multi-Objective, Deep Reinforcement Learning for stock and cryptocurrency single-asset trading: in particular, we consider a Multi-Objective algorithm which generalizes the reward functions and discount factor (i.e., these components are not specified a priori, but incorporated in the learning process). Firstly, using several important assets (BTCUSD, ETHUSDT, XRPUSDT, AAPL, SPY, NIFTY50), we verify the reward generalization property of the proposed Multi-Objective algorithm, and provide preliminary statistical evidence showing increased predictive stability over the corresponding Single-Objective strategy. Secondly, we show that the Multi-Objective algorithm has a clear edge over the corresponding Single-Objective strategy when the reward mechanism is sparse (i.e., when non-null feedback is infrequent over time). Finally, we discuss the generalization properties with respect to the discount factor. The entirety of our code is provided in open-source format.}, author = {Cornalba, Federico and Disselkamp, Constantin and Scassola, Davide and Helf, Christopher}, issn = {1433-3058}, journal = {Neural Computing and Applications}, number = {2}, pages = {617--637}, publisher = {Springer Nature}, title = {{Multi-objective reward generalization: Improving performance of Deep Reinforcement Learning for applications in single-asset trading}}, doi = {10.1007/s00521-023-09033-7}, volume = {36}, year = {2024}, } @article{17887, abstract = {We show convergence of the Navier-Stokes/Allen-Cahn system to a classical sharp interface model for the two-phase flow of two viscous incompressible fluids with same viscosities in a smooth bounded domain in two and three space dimensions as long as a smooth solution of the limit system exists. Moreover, we obtain error estimates with the aid of a relative entropy method. Our results hold provided that the mobility mε>0 in the Allen-Cahn equation tends to zero in a subcritical way, i.e., mε=m0εβ for some β∈(0,2) and m0>0 . The proof proceeds by showing via a relative entropy argument that the solution to the Navier-Stokes/Allen-Cahn system remains close to the solution of a perturbed version of the two-phase flow problem, augmented by an extra mean curvature flow term mεHΓt in the interface motion. In a second step, it is easy to see that the solution to the perturbed problem is close to the original two-phase flow.}, author = {Abels, Helmut and Fischer, Julian L and Moser, Maximilian}, issn = {1432-0673}, journal = {Archive for Rational Mechanics and Analysis}, number = {5}, publisher = {Springer Nature}, title = {{Approximation of classical two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system}}, doi = {10.1007/s00205-024-02020-9}, volume = {248}, year = {2024}, } @article{12485, abstract = {In this paper we introduce the critical variational setting for parabolic stochastic evolution equations of quasi- or semi-linear type. Our results improve many of the abstract results in the classical variational setting. In particular, we are able to replace the usual weak or local monotonicity condition by a more flexible local Lipschitz condition. Moreover, the usual growth conditions on the multiplicative noise are weakened considerably. Our new setting provides general conditions under which local and global existence and uniqueness hold. Moreover, we prove continuous dependence on the initial data. We show that many classical SPDEs, which could not be covered by the classical variational setting, do fit in the critical variational setting. In particular, this is the case for the Cahn-Hilliard equations, tamed Navier-Stokes equations, and Allen-Cahn equation.}, author = {Agresti, Antonio and Veraar, Mark}, issn = {1432-2064}, journal = {Probability Theory and Related Fields}, pages = {957--1015}, publisher = {Springer Nature}, title = {{The critical variational setting for stochastic evolution equations}}, doi = {10.1007/s00440-023-01249-x}, volume = {188}, year = {2024}, } @article{12178, abstract = {In this paper we consider the stochastic primitive equation for geophysical flows subject to transport noise and turbulent pressure. Admitting very rough noise terms, the global existence and uniqueness of solutions to this stochastic partial differential equation are proven using stochastic maximal L² regularity, the theory of critical spaces for stochastic evolution equations, and global a priori bounds. Compared to other results in this direction, we do not need any smallness assumption on the transport noise which acts directly on the velocity field and we also allow rougher noise terms. The adaptation to Stratonovich type noise and, more generally, to variable viscosity and/or conductivity are discussed as well.}, author = {Agresti, Antonio and Hieber, Matthias and Hussein, Amru and Saal, Martin}, issn = {2194-041X}, journal = {Stochastics and Partial Differential Equations: Analysis and Computations}, keywords = {Applied Mathematics, Modeling and Simulation, Statistics and Probability}, pages = {53--133}, publisher = {Springer Nature}, title = {{The stochastic primitive equations with transport noise and turbulent pressure}}, doi = {10.1007/s40072-022-00277-3}, volume = {12}, year = {2024}, } @article{17372, abstract = {In this paper, we investigate the global well-posedness of reaction-diffusion systems with transport noise on the d-dimensional torus. We show new global well-posedness results for a large class of scalar equations (e.g. the Allen-Cahn equation), and dissipative systems (e.g. equations in coagulation dynamics). Moreover, we prove global well-posedness for two weakly dissipative systems: Lotka-Volterra equations for d∈{1,2,3,4} and the Brusselator for d∈{1,2,3}. Many of the results are also new without transport noise. The proofs are based on maximal regularity techniques, positivity results, and sharp blow-up criteria developed in our recent works, combined with energy estimates based on Itô's formula and stochastic Gronwall inequalities. Key novelties include the introduction of new Lζ -coercivity/dissipativity conditions and the development of an Lp(Lq) -framework for systems of reaction-diffusion equations, which are needed when treating dimensions d∈{2,3} in the case of cubic or higher order nonlinearities.}, author = {Agresti, Antonio and Veraar, Mark}, issn = {1095-7154}, journal = {SIAM Journal on Mathematical Analysis}, number = {4}, pages = {4870--4927}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Reaction-diffusion equations with transport noise and critical superlinear diffusion: Global well-posedness of weakly dissipative systems}}, doi = {10.1137/23M1562482}, volume = {56}, year = {2024}, } @article{14884, abstract = {We perform a stochastic homogenization analysis for composite materials exhibiting a random microstructure. Under the assumptions of stationarity and ergodicity, we characterize the Gamma-limit of a micromagnetic energy functional defined on magnetizations taking value in the unit sphere and including both symmetric and antisymmetric exchange contributions. This Gamma-limit corresponds to a micromagnetic energy functional with homogeneous coefficients. We provide explicit formulas for the effective magnetic properties of the composite material in terms of homogenization correctors. Additionally, the variational analysis of the two exchange energy terms is performed in the more general setting of functionals defined on manifold-valued maps with Sobolev regularity, in the case in which the target manifold is a bounded, orientable smooth surface with tubular neighborhood of uniform thickness. Eventually, we present an explicit characterization of minimizers of the effective exchange in the case of magnetic multilayers, providing quantitative evidence of Dzyaloshinskii’s predictions on the emergence of helical structures in composite ferromagnetic materials with stochastic microstructure.}, author = {Davoli, Elisa and D’Elia, Lorenza and Ingmanns, Jonas}, issn = {1432-1467}, journal = {Journal of Nonlinear Science}, number = {2}, publisher = {Springer Nature}, title = {{Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions}}, doi = {10.1007/s00332-023-10005-3}, volume = {34}, year = {2024}, } @inproceedings{19005, abstract = {Causal representation learning promises to extend causal models to hidden causal variables from raw entangled measurements. However, most progress has focused on proving identifiability results in different settings, and we are not aware of any successful real-world application. At the same time, the field of dynamical systems benefited from deep learning and scaled to countless applications but does not allow parameter identification. In this paper, we draw a clear connection between the two and their key assumptions, allowing us to apply identifiable methods developed in causal representation learning to dynamical systems. At the same time, we can leverage scalable differentiable solvers developed for differential equations to build models that are both identifiable and practical. Overall, we learn explicitly controllable models that isolate the trajectory-specific parameters for further downstream tasks such as out-of-distribution classification or treatment effect estimation. We experiment with a wind simulator with partially known factors of variation. We also apply the resulting model to real-world climate data and successfully answer downstream causal questions in line with existing literature on climate change. Code is available at https://github.com/CausalLearningAI/crl-dynamical-systems.}, author = {Yao, Dingling and Muller, Caroline J and Locatello, Francesco}, booktitle = {38th Conference on Neural Information Processing Systems}, issn = {1049-5258}, location = {Vancouver, Canada}, publisher = {Neural Information Processing Systems Foundation}, title = {{Marrying causal representation learning with dynamical systems for science}}, doi = {10.52202/079017-2290}, volume = {37}, year = {2024}, } @article{13129, abstract = {We study the representative volume element (RVE) method, which is a method to approximately infer the effective behavior ahom of a stationary random medium. The latter is described by a coefficient field a(x) generated from a given ensemble ⟨⋅⟩ and the corresponding linear elliptic operator −∇⋅a∇. In line with the theory of homogenization, the method proceeds by computing d=3 correctors (d denoting the space dimension). To be numerically tractable, this computation has to be done on a finite domain: the so-called representative volume element, i.e., a large box with, say, periodic boundary conditions. The main message of this article is: Periodize the ensemble instead of its realizations. By this, we mean that it is better to sample from a suitably periodized ensemble than to periodically extend the restriction of a realization a(x) from the whole-space ensemble ⟨⋅⟩. We make this point by investigating the bias (or systematic error), i.e., the difference between ahom and the expected value of the RVE method, in terms of its scaling w.r.t. the lateral size L of the box. In case of periodizing a(x), we heuristically argue that this error is generically O(L−1). In case of a suitable periodization of ⟨⋅⟩ , we rigorously show that it is O(L−d). In fact, we give a characterization of the leading-order error term for both strategies and argue that even in the isotropic case it is generically non-degenerate. We carry out the rigorous analysis in the convenient setting of ensembles ⟨⋅⟩ of Gaussian type, which allow for a straightforward periodization, passing via the (integrable) covariance function. This setting has also the advantage of making the Price theorem and the Malliavin calculus available for optimal stochastic estimates of correctors. We actually need control of second-order correctors to capture the leading-order error term. This is due to inversion symmetry when applying the two-scale expansion to the Green function. As a bonus, we present a stream-lined strategy to estimate the error in a higher-order two-scale expansion of the Green function.}, author = {Clozeau, Nicolas and Josien, Marc and Otto, Felix and Xu, Qiang}, issn = {1615-3383}, journal = {Foundations of Computational Mathematics}, pages = {1305--1387}, publisher = {Springer Nature}, title = {{Bias in the representative volume element method: Periodize the ensemble instead of its realizations}}, doi = {10.1007/s10208-023-09613-y}, volume = {24}, year = {2024}, } @article{12486, abstract = {This paper is concerned with the problem of regularization by noise of systems of reaction–diffusion equations with mass control. It is known that strong solutions to such systems of PDEs may blow-up in finite time. Moreover, for many systems of practical interest, establishing whether the blow-up occurs or not is an open question. Here we prove that a suitable multiplicative noise of transport type has a regularizing effect. More precisely, for both a sufficiently noise intensity and a high spectrum, the blow-up of strong solutions is delayed up to an arbitrary large time. Global existence is shown for the case of exponentially decreasing mass. The proofs combine and extend recent developments in regularization by noise and in the Lp(Lq)-approach to stochastic PDEs, highlighting new connections between the two areas.}, author = {Agresti, Antonio}, issn = {2194-041X}, journal = {Stochastics and Partial Differential Equations: Analysis and Computations}, pages = {1907--1981}, publisher = {Springer Nature}, title = {{Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations}}, doi = {10.1007/s40072-023-00319-4}, volume = {12}, year = {2024}, } @article{14797, abstract = {We study a random matching problem on closed compact 2 -dimensional Riemannian manifolds (with respect to the squared Riemannian distance), with samples of random points whose common law is absolutely continuous with respect to the volume measure with strictly positive and bounded density. We show that given two sequences of numbers n and m=m(n) of points, asymptotically equivalent as n goes to infinity, the optimal transport plan between the two empirical measures μn and νm is quantitatively well-approximated by (Id,exp(∇hn))#μn where hn solves a linear elliptic PDE obtained by a regularized first-order linearization of the Monge-Ampère equation. This is obtained in the case of samples of correlated random points for which a stretched exponential decay of the α -mixing coefficient holds and for a class of discrete-time Markov chains having a unique absolutely continuous invariant measure with respect to the volume measure.}, author = {Clozeau, Nicolas and Mattesini, Francesco}, issn = {1432-2064}, journal = {Probability Theory and Related Fields}, pages = {485--541}, publisher = {Springer Nature}, title = {{Annealed quantitative estimates for the quadratic 2D-discrete random matching problem}}, doi = {10.1007/s00440-023-01254-0}, volume = {190}, year = {2024}, } @article{15334, abstract = {We consider the sharp interface limit of a Navier-Stokes/Allen Cahn equation in a bounded smooth domain in two space dimensions, in the case of vanishing mobility mε=ε√, where the small parameter ε>0 related to the thickness of the diffuse interface is sent to zero. For well-prepared initial data and sufficiently small times, we rigorously prove convergence to the classical two-phase Navier-Stokes system with surface tension. The idea of the proof is to use asymptotic expansions to construct an approximate solution and to estimate the difference of the exact and approximate solutions with a spectral estimate for the (at the approximate solution) linearized Allen-Cahn operator. In the calculations we use a fractional order ansatz and new ansatz terms in higher orders leading to a suitable ε-scaled and coupled model problem. Moreover, we apply the novel idea of introducing ε-dependent coordinates.}, author = {Abels, Helmut and Fei, Mingwen and Moser, Maximilian}, issn = {1432-0835}, journal = {Calculus of Variations and Partial Differential Equations}, number = {4}, publisher = {Springer Nature}, title = {{Sharp interface limit for a Navier–Stokes/Allen–Cahn system in the case of a vanishing mobility}}, doi = {10.1007/s00526-024-02715-7}, volume = {63}, year = {2024}, }