---
OA_place: publisher
OA_type: diamond
_id: '20032'
abstract:
- lang: eng
  text: We propose Scalable Mechanistic Neural Network (S-MNN), an enhanced neural
    network framework designed for scientific machine learning applications involving
    long temporal sequences. By reformulating the original Mechanistic Neural Network
    (MNN) (Pervez et al., 2024), we reduce the computational time and space complexities
    from cubic and quadratic with respect to the sequence length, respectively, to
    linear. This significant improvement enables efficient modeling of long-term dynamics
    without sacrificing accuracy or interpretability. Extensive experiments demonstrate
    that S-MNN matches the original MNN in precision while substantially reducing
    computational resources. Consequently, S-MNN can drop-in replace the original
    MNN in applications, providing a practical and efficient tool for integrating
    mechanistic bottlenecks into neural network models of complex dynamical systems.
    Source code is available at https://github.com/IST-DASLab/ScalableMNN.
article_processing_charge: No
arxiv: 1
author:
- first_name: Jiale
  full_name: Chen, Jiale
  id: 4d0a9064-1ff6-11ee-9fa6-ec046c604785
  last_name: Chen
  orcid: 0000-0001-5337-5875
- first_name: Dingling
  full_name: Yao, Dingling
  id: d3e02e50-48a8-11ee-8f62-c108061797fa
  last_name: Yao
- first_name: Adeel A
  full_name: Pervez, Adeel A
  id: fca6d90c-d47f-11ee-bc87-93ff51604981
  last_name: Pervez
- first_name: Dan-Adrian
  full_name: Alistarh, Dan-Adrian
  id: 4A899BFC-F248-11E8-B48F-1D18A9856A87
  last_name: Alistarh
  orcid: 0000-0003-3650-940X
- first_name: Francesco
  full_name: Locatello, Francesco
  id: 26cfd52f-2483-11ee-8040-88983bcc06d4
  last_name: Locatello
  orcid: 0000-0002-4850-0683
citation:
  ama: 'Chen J, Yao D, Pervez AA, Alistarh D-A, Locatello F. Scalable mechanistic
    neural networks. In: <i>13th International Conference on Learning Representations</i>.
    ICLR; 2025:63716-63737.'
  apa: 'Chen, J., Yao, D., Pervez, A. A., Alistarh, D.-A., &#38; Locatello, F. (2025).
    Scalable mechanistic neural networks. In <i>13th International Conference on Learning
    Representations</i> (pp. 63716–63737). Singapore, Singapore: ICLR.'
  chicago: Chen, Jiale, Dingling Yao, Adeel A Pervez, Dan-Adrian Alistarh, and Francesco
    Locatello. “Scalable Mechanistic Neural Networks.” In <i>13th International Conference
    on Learning Representations</i>, 63716–37. ICLR, 2025.
  ieee: J. Chen, D. Yao, A. A. Pervez, D.-A. Alistarh, and F. Locatello, “Scalable
    mechanistic neural networks,” in <i>13th International Conference on Learning
    Representations</i>, Singapore, Singapore, 2025, pp. 63716–63737.
  ista: 'Chen J, Yao D, Pervez AA, Alistarh D-A, Locatello F. 2025. Scalable mechanistic
    neural networks. 13th International Conference on Learning Representations. ICLR:
    International Conference on Learning Representations, 63716–63737.'
  mla: Chen, Jiale, et al. “Scalable Mechanistic Neural Networks.” <i>13th International
    Conference on Learning Representations</i>, ICLR, 2025, pp. 63716–37.
  short: J. Chen, D. Yao, A.A. Pervez, D.-A. Alistarh, F. Locatello, in:, 13th International
    Conference on Learning Representations, ICLR, 2025, pp. 63716–63737.
conference:
  end_date: 2025-04-28
  location: Singapore, Singapore
  name: 'ICLR: International Conference on Learning Representations'
  start_date: 2025-04-24
corr_author: '1'
date_created: 2025-07-20T22:02:01Z
date_published: 2025-04-01T00:00:00Z
date_updated: 2025-08-04T08:03:11Z
day: '01'
ddc:
- '000'
department:
- _id: DaAl
- _id: FrLo
external_id:
  arxiv:
  - '2410.06074'
file:
- access_level: open_access
  checksum: 64cfdb12ae3e4e8ba57b1403e1066776
  content_type: application/pdf
  creator: dernst
  date_created: 2025-07-22T07:58:22Z
  date_updated: 2025-07-22T07:58:22Z
  file_id: '20065'
  file_name: 2025_ICLR_Chen.pdf
  file_size: 732745
  relation: main_file
  success: 1
file_date_updated: 2025-07-22T07:58:22Z
has_accepted_license: '1'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 63716-63737
publication: 13th International Conference on Learning Representations
publication_identifier:
  isbn:
  - '9798331320850'
publication_status: published
publisher: ICLR
quality_controlled: '1'
related_material:
  link:
  - relation: software
    url: https://github.com/IST-DASLab/ScalableMNN
scopus_import: '1'
status: public
title: Scalable mechanistic neural networks
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
OA_place: publisher
OA_type: gold
_id: '20817'
abstract:
- lang: eng
  text: We present Mechanistic PDE Networks -- a model for discovery of governing
    partial differential equations from data. Mechanistic PDE Networks represent spatiotemporal
    data as space-time dependent linear partial differential equations in neural network
    hidden representations. The represented PDEs are then solved and decoded for specific
    tasks. The learned PDE representations naturally express the spatiotemporal dynamics
    in data in neural network hidden space, enabling increased modeling power. Solving
    the PDE representations in a compute and memory-efficient way, however, is a significant
    challenge. We develop a native, GPU-capable, parallel, sparse and differentiable
    multigrid solver specialized for linear partial differential equations that acts
    as a module in Mechanistic PDE Networks. Leveraging the PDE solver we propose
    a discovery architecture that can discovers nonlinear PDEs in complex settings,
    while being robust to noise. We validate PDE discovery on a number of PDEs including
    reaction-diffusion and Navier-Stokes equations.
acknowledgement: "AP. This project has received funding from the European Union’s
  Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
  Grant Agreement No. 101034413.\r\nFL. This research was funded in whole or in part
  by the Austrian Science Fund (FWF) 10.55776/COE12. For open access purposes, the
  author has applied a CC BY public\r\ncopyright license to any author accepted manuscript
  version arising from this submission."
alternative_title:
- PMLR
article_processing_charge: No
arxiv: 1
author:
- first_name: Adeel A
  full_name: Pervez, Adeel A
  id: fca6d90c-d47f-11ee-bc87-93ff51604981
  last_name: Pervez
- first_name: Efstratios
  full_name: Gavves, Efstratios
  last_name: Gavves
- first_name: Francesco
  full_name: Locatello, Francesco
  id: 26cfd52f-2483-11ee-8040-88983bcc06d4
  last_name: Locatello
  orcid: 0000-0002-4850-0683
citation:
  ama: 'Pervez AA, Gavves E, Locatello F. Mechanistic PDE networks for discovery of
    governing equations. In: <i>42nd International Conference on Machine Learning</i>.
    Vol 267. ML Research Press; 2025:48962-48973.'
  apa: 'Pervez, A. A., Gavves, E., &#38; Locatello, F. (2025). Mechanistic PDE networks
    for discovery of governing equations. In <i>42nd International Conference on Machine
    Learning</i> (Vol. 267, pp. 48962–48973). Vancouver, Canada: ML Research Press.'
  chicago: Pervez, Adeel A, Efstratios Gavves, and Francesco Locatello. “Mechanistic
    PDE Networks for Discovery of Governing Equations.” In <i>42nd International Conference
    on Machine Learning</i>, 267:48962–73. ML Research Press, 2025.
  ieee: A. A. Pervez, E. Gavves, and F. Locatello, “Mechanistic PDE networks for discovery
    of governing equations,” in <i>42nd International Conference on Machine Learning</i>,
    Vancouver, Canada, 2025, vol. 267, pp. 48962–48973.
  ista: 'Pervez AA, Gavves E, Locatello F. 2025. Mechanistic PDE networks for discovery
    of governing equations. 42nd International Conference on Machine Learning. ICML:
    International Conference on Machine Learning, PMLR, vol. 267, 48962–48973.'
  mla: Pervez, Adeel A., et al. “Mechanistic PDE Networks for Discovery of Governing
    Equations.” <i>42nd International Conference on Machine Learning</i>, vol. 267,
    ML Research Press, 2025, pp. 48962–73.
  short: A.A. Pervez, E. Gavves, F. Locatello, in:, 42nd International Conference
    on Machine Learning, ML Research Press, 2025, pp. 48962–48973.
conference:
  end_date: 2025-07-19
  location: Vancouver, Canada
  name: 'ICML: International Conference on Machine Learning'
  start_date: 2025-07-13
corr_author: '1'
date_created: 2025-12-14T23:02:04Z
date_published: 2025-05-01T00:00:00Z
date_updated: 2026-09-16T07:17:18Z
day: '01'
ddc:
- '000'
department:
- _id: FrLo
ec_funded: 1
external_id:
  arxiv:
  - '2502.18377'
file:
- access_level: open_access
  checksum: 933cb673fb41416f537278fb990df6c3
  content_type: application/pdf
  creator: dernst
  date_created: 2025-12-16T12:21:49Z
  date_updated: 2025-12-16T12:21:49Z
  file_id: '20827'
  file_name: 2025_ICML_Pervez.pdf
  file_size: 993381
  relation: main_file
  success: 1
file_date_updated: 2025-12-16T12:21:49Z
has_accepted_license: '1'
intvolume: '       267'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 48962-48973
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
- _id: a392d8f0-b034-11f1-b88e-d3025c6734f6
  grant_number: COE12
  name: Bilateral Artificial Intelligence (Locatello)
publication: 42nd International Conference on Machine Learning
publication_identifier:
  eissn:
  - 2640-3498
publication_status: published
publisher: ML Research Press
quality_controlled: '1'
related_material:
  link:
  - relation: software
    url: https://github.com/ alpz/mech-nn-discovery-pde
scopus_import: '1'
status: public
title: Mechanistic PDE networks for discovery of governing equations
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 267
year: '2025'
...
---
OA_place: publisher
OA_type: diamond
_id: '18114'
abstract:
- lang: eng
  text: This paper presents Mechanistic Neural Networks, a neural network design for
    machine learning applications in the sciences. It incorporates a new Mechanistic
    Block in standard architectures to explicitly learn governing differential equations
    as representations, revealing the underlying dynamics of data and enhancing interpretability
    and efficiency in data modeling. Central to our approach is a novel Relaxed Linear
    Programming Solver (NeuRLP) inspired by a technique that reduces solving linear
    ODEs to solving linear programs. This integrates well with neural networks and
    surpasses the limitations of traditional ODE solvers enabling scalable GPU parallel
    processing. Overall, Mechanistic Neural Networks demonstrate their versatility
    for scientific machine learning applications, adeptly managing tasks from equation
    discovery to dynamic systems modeling. We prove their comprehensive capabilities
    in analyzing and interpreting complex scientific data across various applications,
    showing significant performance against specialized state-of-the-art methods.
    Source code is available at https://github.com/alpz/mech-nn.
alternative_title:
- PMLR
article_processing_charge: No
arxiv: 1
author:
- first_name: Adeel A
  full_name: Pervez, Adeel A
  id: fca6d90c-d47f-11ee-bc87-93ff51604981
  last_name: Pervez
- first_name: Francesco
  full_name: Locatello, Francesco
  id: 26cfd52f-2483-11ee-8040-88983bcc06d4
  last_name: Locatello
  orcid: 0000-0002-4850-0683
- first_name: Efstratios
  full_name: Gavves, Efstratios
  last_name: Gavves
citation:
  ama: 'Pervez AA, Locatello F, Gavves E. Mechanistic neural networks for scientific
    machine learning. In: <i>Proceedings of the 41st International Conference on Machine
    Learning</i>. Vol 235. ML Research Press; 2024:40484-40501.'
  apa: 'Pervez, A. A., Locatello, F., &#38; Gavves, E. (2024). Mechanistic neural
    networks for scientific machine learning. In <i>Proceedings of the 41st International
    Conference on Machine Learning</i> (Vol. 235, pp. 40484–40501). Vienna, Austria:
    ML Research Press.'
  chicago: Pervez, Adeel A, Francesco Locatello, and Efstratios Gavves. “Mechanistic
    Neural Networks for Scientific Machine Learning.” In <i>Proceedings of the 41st
    International Conference on Machine Learning</i>, 235:40484–501. ML Research Press,
    2024.
  ieee: A. A. Pervez, F. Locatello, and E. Gavves, “Mechanistic neural networks for
    scientific machine learning,” in <i>Proceedings of the 41st International Conference
    on Machine Learning</i>, Vienna, Austria, 2024, vol. 235, pp. 40484–40501.
  ista: 'Pervez AA, Locatello F, Gavves E. 2024. Mechanistic neural networks for scientific
    machine learning. Proceedings of the 41st International Conference on Machine
    Learning. ICML: International Conference on Machine Learning, PMLR, vol. 235,
    40484–40501.'
  mla: Pervez, Adeel A., et al. “Mechanistic Neural Networks for Scientific Machine
    Learning.” <i>Proceedings of the 41st International Conference on Machine Learning</i>,
    vol. 235, ML Research Press, 2024, pp. 40484–501.
  short: A.A. Pervez, F. Locatello, E. Gavves, in:, Proceedings of the 41st International
    Conference on Machine Learning, ML Research Press, 2024, pp. 40484–40501.
conference:
  end_date: 2024-07-27
  location: Vienna, Austria
  name: 'ICML: International Conference on Machine Learning'
  start_date: 2024-07-21
date_created: 2024-09-22T22:01:43Z
date_published: 2024-09-01T00:00:00Z
date_updated: 2026-06-18T17:59:46Z
day: '01'
ddc:
- '000'
department:
- _id: FrLo
external_id:
  arxiv:
  - '2402.13077'
intvolume: '       235'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2402.13077
month: '09'
oa: 1
oa_version: Published Version
page: 40484-40501
publication: Proceedings of the 41st International Conference on Machine Learning
publication_identifier:
  eissn:
  - 2640-3498
publication_status: published
publisher: ML Research Press
quality_controlled: '1'
related_material:
  link:
  - relation: software
    url: https://github.com/alpz/mech-nn
scopus_import: '1'
status: public
title: Mechanistic neural networks for scientific machine learning
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 235
year: '2024'
...