Global Convergence of Deep Galerkin and PINN Methods for Solving Partial Differential Equations.

Samuel N. Cohen

Deqing Jiang Justin A. Sirignano Samuel N. Cohen Global Convergence of Deep Galerkin and PINN Methods for Solving Partial Differential Equations. 2026 620-645 17 SIAM J. Financial Math. 2 https://doi.org/10.1137/24m1701502 db/journals/siamfm/siamfm17.html#JiangSC26 streams/journals/siamfm

Alexandre Bloch Samuel N. Cohen Terry J. Lyons Joël Mouterde Benjamin Walker 0001 The Exponentially Weighted Signature. 2026 March abs/2603.19198 CoRR https://doi.org/10.48550/arXiv.2603.19198 db/journals/corr/corr2603.html#abs-2603-19198 streams/journals/corr

Samuel N. Cohen Filippo de Feo Jackson Hebner Justin A. Sirignano Deep Hilbert-Galerkin Methods for Infinite-Dimensional PDEs and Optimal Control. 2026 March abs/2603.19463 CoRR https://doi.org/10.48550/arXiv.2603.19463 db/journals/corr/corr2603.html#abs-2603-19463 streams/journals/corr

Louis J. M. Aslett Andreea Avramescu Nicholas Bakewell Isabel Birds Louise Bowler Michael P. J. Camilleri Sheng-Chia Chung David A. Clifton Samuel N. Cohen Nathan Constantine-Cooke Eric G. Daub Shaun M. Davidson Spiros C. Denaxas Karla Diaz-Ordaz Richard Feltbower Suzy Gallier Stephen Gardiner Francesca Gasperoni Robert J. B. Goudie Rebecca E. Green Marlous S. Hall Chris Holmes 0001 John R. Hurst Mark M. Iles João Jorge Emma Karoune Ruth H. Keogh Ruairidh King Ruth King Paul D. W. Kirk Roman Klapaukh Samaneh Kouchaki Alvina Grace Lai Nathan Lea Clemence Leyrat Kezhi Li Watjana Lilaonitkul Huiqi Y. Lu Terry Lyons Ann-Marie Mallon Andrew A. Manderson Nicolò Margaritella Joshua Matteson Sam Morley Hannah Nicholls Martin T. O'Reilly Christina Pagel Edward Palmer Jack Roberts Timothy J. Roberts David S. Robertson 0001 James Robinson Patrick Rockenschaub Roy A. Ruddle Elizabeth Sapey Luis Santos Andrew A. S. Soltan Fang Gao-Smith Colin Starr Oliver Strickson Li Su Mia S. Tackney Johan Hilge Thygesen Ana Torralbo Alice M. Turner Catalina A. Vallejos Chenyang Wang Kirstie J. Whitaker Tony Whitehouse David R. Westhead Wai Keong Wong Yue Wu 0016 Lingyi Yang Xiaoxu Zou DECOVID: A UK Two-Center Harmonized Database of Acute Care Electronic Health Records for COVID-19 Research. 195 2025 10 Data 12 https://doi.org/10.3390/data10120195 db/journals/data/data10.html#AslettABBBCCCCCDDDDFGGG25 streams/journals/data

Samuel N. Cohen Christoph Knochenhauer Alexander Merkel Optimal Adaptive Control with Separable Drift Uncertainty. 1348-1373 2025 63 SIAM J. Control. Optim. 2 https://doi.org/10.1137/23m1616236 db/journals/siamco/siamco63.html#CohenKM25 streams/journals/siamco

Gholamali Aminian Amir R. Asadi Tian Li 0005 Ahmad Beirami Gesine Reinert Samuel N. Cohen Generalization and Robustness of the Tilted Empirical Risk. 2025 ICML https://proceedings.mlr.press/v267/aminian25a.html https://openreview.net/forum?id=Wvc6d6926j conf/icml/2025 db/conf/icml/icml2025.html#AminianA0BRC25

Samuel N. Cohen Jackson Hebner Deqing Jiang Justin A. Sirignano Neural Actor-Critic Methods for Hamilton-Jacobi-Bellman PDEs: Asymptotic Analysis and Numerical Studies. 2025 July abs/2507.06428 CoRR https://doi.org/10.48550/arXiv.2507.06428 db/journals/corr/corr2507.html#abs-2507-06428 streams/journals/corr

Gholamali Aminian Yixuan He 0001 Gesine Reinert Lukasz Szpruch Samuel N. Cohen Generalization Error of Graph Neural Networks in the Mean-field Regime. 2024 ICML https://proceedings.mlr.press/v235/aminian24a.html https://openreview.net/forum?id=8h0x12p3zq conf/icml/2024 db/conf/icml/icml2024.html#AminianHRSC24 1359-1391

Gholamali Aminian Yixuan He 0001 Gesine Reinert Lukasz Szpruch Samuel N. Cohen Generalization Error of Graph Neural Networks in the Mean-field Regime. 2024 abs/2402.07025 CoRR https://doi.org/10.48550/arXiv.2402.07025 db/journals/corr/corr2402.html#abs-2402-07025

Gholamali Aminian Amir R. Asadi Tian Li 0005 Ahmad Beirami Gesine Reinert Samuel N. Cohen Generalization Error of the Tilted Empirical Risk. 2024 abs/2409.19431 CoRR https://doi.org/10.48550/arXiv.2409.19431 db/journals/corr/corr2409.html#abs-2409-19431 streams/journals/corr

Gholamali Aminian Lukasz Szpruch Samuel N. Cohen Understanding Transfer Learning via Mean-field Analysis. 2024 abs/2410.17128 CoRR https://doi.org/10.48550/arXiv.2410.17128 db/journals/corr/corr2410.html#abs-2410-17128 streams/journals/corr

Samuel N. Cohen Deqing Jiang Justin A. Sirignano Neural Q-learning for solving PDEs. 236:1-236:49 2023 24 J. Mach. Learn. Res. https://jmlr.org/papers/v24/22-1075.html db/journals/jmlr/jmlr24.html#CohenJS23

Samuel N. Cohen Marc Sabate Vidales David Siska Lukasz Szpruch Inefficiency of CFMs: Hedging Perspective and Agent-Based Simulations. 303-319 2023 FC Workshops https://doi.org/10.1007/978-3-031-48806-1_20 conf/fc/2023w db/conf/fc/fc2023w.html#CohenVSS23

Deqing Jiang Justin A. Sirignano Samuel N. Cohen Global Convergence of Deep Galerkin and PINNs Methods for Solving Partial Differential Equations. 2023 abs/2305.06000 CoRR https://doi.org/10.48550/arXiv.2305.06000 db/journals/corr/corr2305.html#abs-2305-06000

Gholamali Aminian Samuel N. Cohen Lukasz Szpruch Mean-field Analysis of Generalization Errors. 2023 abs/2306.11623 CoRR https://doi.org/10.48550/arXiv.2306.11623 db/journals/corr/corr2306.html#abs-2306-11623

Samuel N. Cohen Deqing Jiang Justin A. Sirignano Neural Q-learning for solving elliptic PDEs. 2022 abs/2203.17128 CoRR https://doi.org/10.48550/arXiv.2203.17128 db/journals/corr/corr2203.html#abs-2203-17128

James Jordon Lukasz Szpruch Florimond Houssiau Mirko Bottarelli Giovanni Cherubin Carsten Maple Samuel N. Cohen Adrian Weller Synthetic Data - what, why and how? 2022 abs/2205.03257 CoRR https://doi.org/10.48550/arXiv.2205.03257 db/journals/corr/corr2205.html#abs-2205-03257

Florimond Houssiau James Jordon Samuel N. Cohen Owen Daniel Andrew Elliott James Geddes Callum D. Mole Camila Rangel Smith Lukasz Szpruch TAPAS: a Toolbox for Adversarial Privacy Auditing of Synthetic Data. 2022 abs/2211.06550 CoRR https://doi.org/10.48550/arXiv.2211.06550 db/journals/corr/corr2211.html#abs-2211-06550

Florimond Houssiau Samuel N. Cohen Lukasz Szpruch Owen Daniel Michaela G. Lawrence Robin Mitra Henry Wilde Callum D. Mole A Framework for Auditable Synthetic Data Generation. 2022 abs/2211.11540 CoRR https://doi.org/10.48550/arXiv.2211.11540 db/journals/corr/corr2211.html#abs-2211-11540

Haoyang Cao Samuel N. Cohen Lukasz Szpruch Identifiability in inverse reinforcement learning. 12362-12373 2021 NeurIPS https://proceedings.neurips.cc/paper/2021/hash/671f0311e2754fcdd37f70a8550379bc-Abstract.html conf/nips/2021 db/conf/nips/neurips2021.html#CaoCS21

Haoyang Cao Samuel N. Cohen Lukasz Szpruch Identifiability in inverse reinforcement learning. 2021 abs/2106.03498 CoRR https://arxiv.org/abs/2106.03498 db/journals/corr/corr2106.html#abs-2106-03498

Andrew L. Allan Samuel N. Cohen Parameter Uncertainty in the Kalman-Bucy Filter. 1646-1671 2019 57 SIAM J. Control. Optim. 3 https://doi.org/10.1137/18M1167693 https://www.wikidata.org/entity/Q127872794 db/journals/siamco/siamco57.html#AllanC19

Samuel N. Cohen Victor Fedyashov Nash equilibria for nonzero-sum ergodic stochastic differential games. 977-994 2017 54 J. Appl. Probab. 4 https://doi.org/10.1017/jpr.2017.48 db/journals/jap/jap54.html#CohenF17

Robert J. Elliott Tak Kuen Siu Samuel N. Cohen Backward stochastic difference equations for dynamic convex risk measures on a binomial tree. 771-785 2015 52 J. Appl. Probab. 3 https://doi.org/10.1017/S0021900200113427 db/journals/jap/jap52.html#ElliottSC15

Samuel N. Cohen Undiscounted Markov Chain BSDEs to Stopping Times. 262-281 2014 51 J. Appl. Probab. 1 https://doi.org/10.1017/S0021900200010226 db/journals/jap/jap51.html#Cohen14

Samuel N. Cohen Ying Hu Ergodic BSDEs Driven by Markov Chains. 4138-4168 2013 51 SIAM J. Control. Optim. 5 https://doi.org/10.1137/120885875 db/journals/siamco/siamco51.html#CohenH13

Samuel N. Cohen Robert J. Elliott Backward Stochastic Difference Equations and Nearly Time-Consistent Nonlinear Expectations. 125-139 2011 49 SIAM J. Control. Optim. 1 https://doi.org/10.1137/090763688 db/journals/siamco/siamco49.html#CohenE11

Andrew L. Allan Gholamali Aminian Amir R. Asadi Louis J. M. Aslett Andreea Avramescu Nicholas Bakewell Ahmad Beirami Isabel Birds Alexandre Bloch Mirko Bottarelli Louise Bowler Michael P. J. Camilleri Haoyang Cao Giovanni Cherubin Sheng-Chia Chung David A. Clifton Nathan Constantine-Cooke Owen Daniel Eric G. Daub Shaun M. Davidson Spiros C. Denaxas Karla Diaz-Ordaz Andrew Elliott Robert J. Elliott Victor Fedyashov Richard Feltbower Filippo de Feo Suzy Gallier Fang Gao-Smith Stephen Gardiner Francesca Gasperoni James Geddes Robert J. B. Goudie Rebecca E. Green Marlous S. Hall Yixuan He 0001 Jackson Hebner Christopher C. HolmesChris Holmes 0001 Florimond Houssiau Ying Hu John R. Hurst Mark M. Iles Deqing Jiang James Jordon João Jorge Emma Karoune Ruth H. Keogh Ruairidh King Ruth King Paul D. W. Kirk Roman Klapaukh Christoph Knochenhauer Samaneh Kouchaki Alvina Grace Lai Michaela G. Lawrence Nathan Lea Clemence Leyrat Kezhi Li Tian Li 0005 Watjana Lilaonitkul Huiqi Y. Lu Terry Lyons Terry J. Lyons Ann-Marie Mallon Andrew A. Manderson Carsten Maple Nicolò Margaritella Joshua Matteson Alexander Merkel Robin Mitra Callum D. Mole Samuel MorleySam Morley Joël Mouterde Hannah Nicholls Martin T. O'Reilly Christina Pagel Edward Palmer Gesine Reinert Jack Roberts Timothy J. Roberts David S. Robertson 0001 James Robinson Patrick Rockenschaub Roy A. Ruddle Luís SantosLuis Santos Elizabeth Sapey Justin A. Sirignano David Siska Tak Kuen Siu Camila Rangel Smith Andrew A. S. Soltan Colin Starr Oliver T. StricksonOliver Strickson Li Su Lukasz Szpruch Mia S. Tackney Johan Hilge Thygesen Ana Torralbo Alice M. Turner Catalina A. Vallejos Marc Sabate Vidales Benjamin Walker 0001 Chenyang Wang Adrian Weller David R. Westhead Kirstie J. Whitaker Tony Whitehouse Henry Wilde Wai Keong Wong Yue Wu 0016 Lingyi Yang Xiaoxu Zou