Multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation overcome the curse of dimensionality when approximating semilinear parabolic partial differential equations in Lp-sense.

Ariel Neufeld

Ariel Neufeld Tuan Anh Nguyen Multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation overcome the curse of dimensionality when approximating semilinear parabolic partial differential equations in Lp-sense. 2026 117736 487 J. Comput. Appl. Math. https://doi.org/10.1016/j.cam.2026.117736 db/journals/jcam/jcam487.html#NeufeldN26 streams/journals/jcam

Mathieu Laurière Ariel Neufeld Kyunghyun Park Robust Q-learning for mean-field control under Wasserstein uncertainty in common noise. 2026 June abs/2606.20356 CoRR https://doi.org/10.48550/arXiv.2606.20356 db/journals/corr/corr2606.html#abs-2606-20356 streams/journals/corr

Ariel Neufeld Philipp Schmocker Sizhou Wu Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs. 108556 2025 143 Commun. Nonlinear Sci. Numer. Simul. https://doi.org/10.1016/j.cnsns.2024.108556 db/journals/cnsns/cnsns143.html#NeufeldSW25 streams/journals/cnsns

Ariel Neufeld Julian Sester Bounding the difference between the values of robust and non-robust Markov decision problems. 558-571 2025 62 J. Appl. Probab. 2 https://doi.org/10.1017/jpr.2024.88 db/journals/jap/jap62.html#NeufeldS25 streams/journals/jap

Ariel Neufeld Tuan Anh Nguyen Sizhou Wu Multilevel Picard approximations overcome the curse of dimensionality in the numerical approximation of general semilinear PDEs with gradient-dependent nonlinearities. 101946 2025 90 J. Complex. https://doi.org/10.1016/j.jco.2025.101946 db/journals/jc/jc90.html#NeufeldNW25 streams/journals/jc

Dong-Young Lim Ariel Neufeld Sotirios Sabanis Ying Zhang 0037 Langevin Dynamics Based Algorithm e-TH<i>ε</i>O POULA for Stochastic Optimization Problems with Discontinuous Stochastic Gradient. 2333-2374 2025 50 Math. Oper. Res. 3 https://doi.org/10.1287/moor.2022.0307 db/journals/mor/mor50.html#LimNSZ25 streams/journals/mor

Hari Hara Suthan Chittoor Paul Robert Griffin Ariel Neufeld Jayne Thompson Mile Gu QuLTSF: Long-Term Time Series Forecasting with Quantum Machine Learning. 824-829 2025 ICAART (1) https://doi.org/10.5220/0013395500003890 conf/icaart/2025-1 db/conf/icaart/icaart2025-1.html#ChittoorGNTG25

Ariel Neufeld Tuan Anh Nguyen Philipp Schmocker Multilevel Picard approximations for McKean-Vlasov stochastic differential equations with nonconstant diffusion. 2025 February abs/2502.03205 CoRR https://doi.org/10.48550/arXiv.2502.03205 db/journals/corr/corr2502.html#abs-2502-03205 streams/journals/corr

Zeyi Chen Ariel Neufeld Qikun Xiang Provably convergent stochastic fixed-point algorithm for free-support Wasserstein barycenter of continuous non-parametric measures. 2025 May abs/2505.24384 CoRR https://doi.org/10.48550/arXiv.2505.24384 db/journals/corr/corr2505.html#abs-2505-24384 streams/journals/corr

Anastasis Kratsios Ariel Neufeld Philipp Schmocker Generative Neural Operators of Log-Complexity Can Simultaneously Solve Infinitely Many Convex Programs. 2025 August abs/2508.14995 CoRR https://doi.org/10.48550/arXiv.2508.14995 db/journals/corr/corr2508.html#abs-2508-14995 streams/journals/corr

Ariel Neufeld Philipp Schmocker Viet Khoa Tran Approximation rates of quantum neural networks for periodic functions via Jackson's inequality. 2025 November abs/2511.16149 CoRR https://doi.org/10.48550/arXiv.2511.16149 db/journals/corr/corr2511.html#abs-2511-16149 streams/journals/corr

Ariel Neufeld Julian Sester Robust Q-learning algorithm for Markov decision processes under Wasserstein uncertainty. 111825 2024 168 Autom. https://doi.org/10.1016/j.automatica.2024.111825 db/journals/automatica/automatica168.html#NeufeldS24 streams/journals/automatica

Shunan Sheng Qikun Xiang Ido Nevat Ariel Neufeld Binary spatial random field reconstruction from non-Gaussian inhomogeneous time-series observations. 612-636 2024 361 J. Frankl. Inst. 2 https://doi.org/10.1016/j.jfranklin.2023.12.016 db/journals/jfi/jfi361.html#ShengXNN24

Ariel Neufeld Julian Sester Daiying Yin Detecting Data-Driven Robust Statistical Arbitrage Strategies with Deep Neural Networks. 436-472 2024 15 SIAM J. Financial Math. 2 https://doi.org/10.1137/22m1487928 db/journals/siamfm/siamfm15.html#NeufeldSY24

Ariel Neufeld Tuan Anh Nguyen Rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of gradient-dependent semilinear heat equations. 2024 abs/2403.09200 CoRR https://doi.org/10.48550/arXiv.2403.09200 db/journals/corr/corr2403.html#abs-2403-09200

Daniel Bartl Ariel Neufeld Kyunghyun Park Numerical method for nonlinear Kolmogorov PDEs via sensitivity analysis. 2024 abs/2403.11910 CoRR https://doi.org/10.48550/arXiv.2403.11910 db/journals/corr/corr2403.html#abs-2403-11910

Ariel Neufeld Philipp Schmocker Sizhou Wu Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs with infinite activity. 2024 abs/2405.05192 CoRR https://doi.org/10.48550/arXiv.2405.05192 db/journals/corr/corr2405.html#abs-2405-05192

Luxu Liang Ariel Neufeld Ying Zhang Non-asymptotic convergence analysis of the stochastic gradient Hamiltonian Monte Carlo algorithm with discontinuous stochastic gradient with applications to training of ReLU neural networks. 2024 abs/2409.17107 CoRR https://doi.org/10.48550/arXiv.2409.17107 db/journals/corr/corr2409.html#abs-2409-17107 streams/journals/corr

Ariel Neufeld Tuan Anh Nguyen Multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation overcome the curse of dimensionality when approximating semilinear parabolic partial differential equations in L<sup>p</sup>-sense. 2024 abs/2409.20431 CoRR https://doi.org/10.48550/arXiv.2409.20431 db/journals/corr/corr2409.html#abs-2409-20431 streams/journals/corr

Ariel Neufeld Philipp Schmocker Universal approximation results for neural networks with non-polynomial activation function over non-compact domains. 2024 abs/2410.14759 CoRR https://doi.org/10.48550/arXiv.2410.14759 db/journals/corr/corr2410.html#abs-2410-14759 streams/journals/corr

Ariel Neufeld Philipp Schmocker Solving stochastic partial differential equations using neural networks in the Wiener chaos expansion. 2024 abs/2411.03384 CoRR https://doi.org/10.48550/arXiv.2411.03384 db/journals/corr/corr2411.html#abs-2411-03384 streams/journals/corr

Hari Hara Suthan Chittoor Paul Robert Griffin Ariel Neufeld Jayne Thompson Mile Gu QuLTSF: Long-Term Time Series Forecasting with Quantum Machine Learning. 2024 abs/2412.13769 CoRR https://doi.org/10.48550/arXiv.2412.13769 db/journals/corr/corr2412.html#abs-2412-13769 streams/journals/corr

Christian Beck Sebastian Becker Patrick Cheridito Arnulf Jentzen Ariel Neufeld An efficient Monte Carlo scheme for Zakai equations. 107438 2023 November 126 Commun. Nonlinear Sci. Numer. Simul. https://doi.org/10.1016/j.cnsns.2023.107438 db/journals/cnsns/cnsns126.html#BeckBCJN23

Ariel Neufeld Antonis Papapantoleon Qikun Xiang Model-Free Bounds for Multi-Asset Options Using Option-Implied Information and Their Exact Computation. 2051-2068 2023 April 69 Manag. Sci. 4 https://doi.org/10.1287/mnsc.2022.4456 db/journals/mansci/mansci69.html#NeufeldPX23

Ariel Neufeld Julian Sester A Deep Learning Approach to Data-Driven Model-Free Pricing and to Martingale Optimal Transport. 3172-3189 2023 May 69 IEEE Trans. Inf. Theory 5 https://doi.org/10.1109/TIT.2022.3229845 db/journals/tit/tit69.html#NeufeldS23

Michel Baes Calypso Herrera Ariel Neufeld Pierre Ruyssen Low-Rank Plus Sparse Decomposition of Covariance Matrices Using Neural Network Parametrization. 171-185 2023 34 IEEE Trans. Neural Networks Learn. Syst. 1 https://doi.org/10.1109/TNNLS.2021.3091598 db/journals/tnn/tnn34.html#BaesHNR23

Yongming Li Ariel Neufeld Quantum Monte Carlo algorithm for solving Black-Scholes PDEs for high-dimensional option pricing in finance and its proof of overcoming the curse of dimensionality. 2023 abs/2301.09241 CoRR https://doi.org/10.48550/arXiv.2301.09241 db/journals/corr/corr2301.html#abs-2301-09241

Ariel Neufeld Julian Sester Neural networks can detect model-free static arbitrage strategies. 2023 abs/2306.16422 CoRR https://doi.org/10.48550/arXiv.2306.16422 db/journals/corr/corr2306.html#abs-2306-16422

Ariel Neufeld Qikun Xiang Feasible approximation of matching equilibria for large-scale matching for teams problems. 2023 abs/2308.03550 CoRR https://doi.org/10.48550/arXiv.2308.03550 db/journals/corr/corr2308.html#abs-2308-03550

Ariel Neufeld Sizhou Wu Multilevel Picard algorithm for general semilinear parabolic PDEs with gradient-dependent nonlinearities. 2023 abs/2310.12545 CoRR https://doi.org/10.48550/arXiv.2310.12545 db/journals/corr/corr2310.html#abs-2310-12545

Ariel Neufeld Tuan Anh Nguyen Sizhou Wu Deep ReLU neural networks overcome the curse of dimensionality when approximating semilinear partial integro-differential equations. 2023 abs/2310.15581 CoRR https://doi.org/10.48550/arXiv.2310.15581 db/journals/corr/corr2310.html#abs-2310-15581

Ariel Neufeld Tuan Anh Nguyen Sizhou Wu Multilevel Picard approximations overcome the curse of dimensionality in the numerical approximation of general semilinear PDEs with gradient-dependent nonlinearities. 2023 abs/2311.11579 CoRR https://doi.org/10.48550/arXiv.2311.11579 db/journals/corr/corr2311.html#abs-2311-11579

Ariel Neufeld Tuan Anh Nguyen Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean-Vlasov stochastic differential equations. 2023 abs/2312.07042 CoRR https://doi.org/10.48550/arXiv.2312.07042 db/journals/corr/corr2312.html#abs-2312-07042

Ariel Neufeld Philipp Schmocker Universal Approximation Property of Random Neural Networks. 2023 abs/2312.08410 CoRR https://doi.org/10.48550/arXiv.2312.08410 db/journals/corr/corr2312.html#abs-2312-08410

Ariel Neufeld Qikun Xiang Numerical method for feasible and approximately optimal solutions of multi-marginal optimal transport beyond discrete measures. 2022 abs/2203.01633 CoRR https://doi.org/10.48550/arXiv.2203.01633 db/journals/corr/corr2203.html#abs-2203-01633

Ariel Neufeld Julian Sester Daiying Yin Detecting data-driven robust statistical arbitrage strategies with deep neural networks. 2022 abs/2203.03179 CoRR https://doi.org/10.48550/arXiv.2203.03179 db/journals/corr/corr2203.html#abs-2203-03179

Shunan Sheng Qikun Xiang Ido Nevat Ariel Neufeld Binary Spatial Random Field Reconstruction from Non-Gaussian Inhomogeneous Time-series Observations. 2022 abs/2204.03343 CoRR https://doi.org/10.48550/arXiv.2204.03343 db/journals/corr/corr2204.html#abs-2204-03343

Ariel Neufeld Qikun Xiang Numerical method for approximately optimal solutions of two-stage distributionally robust optimization with marginal constraints. 2022 abs/2205.05315 CoRR https://doi.org/10.48550/arXiv.2205.05315 db/journals/corr/corr2205.html#abs-2205-05315

Ariel Neufeld Sizhou Wu Multilevel Picard approximation algorithm for semilinear partial integro-differential equations and its complexity analysis. 2022 abs/2205.09639 CoRR https://doi.org/10.48550/arXiv.2205.09639 db/journals/corr/corr2205.html#abs-2205-09639

Ariel Neufeld Julian Sester Mario Sikic Markov Decision Processes under Model Uncertainty. 2022 abs/2206.06109 CoRR https://doi.org/10.48550/arXiv.2206.06109 db/journals/corr/corr2206.html#abs-2206-06109

Ariel Neufeld Matthew Ng Cheng En Ying Zhang 0037 Non-asymptotic convergence bounds for modified tamed unadjusted Langevin algorithm in non-convex setting. 2022 abs/2207.02600 CoRR https://doi.org/10.48550/arXiv.2207.02600 db/journals/corr/corr2207.html#abs-2207-02600

Ariel Neufeld Philipp Schmocker Chaotic Hedging with Iterated Integrals and Neural Networks. 2022 abs/2209.10166 CoRR https://doi.org/10.48550/arXiv.2209.10166 db/journals/corr/corr2209.html#abs-2209-10166

Ariel Neufeld Julian Sester Robust Q-learning Algorithm for Markov Decision Processes under Wasserstein Uncertainty. 2022 abs/2210.00898 CoRR https://doi.org/10.48550/arXiv.2210.00898 db/journals/corr/corr2210.html#abs-2210-00898

Dong-Young Lim Ariel Neufeld Sotirios Sabanis Ying Zhang 0037 Langevin dynamics based algorithm e-THεO POULA for stochastic optimization problems with discontinuous stochastic gradient. 2022 abs/2210.13193 CoRR https://doi.org/10.48550/arXiv.2210.13193 db/journals/corr/corr2210.html#abs-2210-13193

Christian Beck Sebastian Becker Patrick Cheridito Arnulf Jentzen Ariel Neufeld An efficient Monte Carlo scheme for Zakai equations. 2022 abs/2210.13530 CoRR https://doi.org/10.48550/arXiv.2210.13530 db/journals/corr/corr2210.html#abs-2210-13530

Ariel Neufeld Julian Sester Model-Free Price Bounds Under Dynamic Option Trading. 1307-1339 2021 12 SIAM J. Financial Math. 4 https://doi.org/10.1137/21M1390013 db/journals/siamfm/siamfm12.html#NeufeldS21

Christian Beck Sebastian Becker Patrick Cheridito Arnulf Jentzen Ariel Neufeld Deep Splitting Method for Parabolic PDEs. A3135-A3154 2021 43 SIAM J. Sci. Comput. 5 https://doi.org/10.1137/19M1297919 https://www.wikidata.org/entity/Q114074224 db/journals/siamsc/siamsc43.html#BeckBCJN21

Ariel Neufeld Julian Sester A deep learning approach to data-driven model-free pricing and to martingale optimal transport. 2021 abs/2103.11435 CoRR https://arxiv.org/abs/2103.11435 db/journals/corr/corr2103.html#abs-2103-11435

Dong-Young Lim Ariel Neufeld Sotirios Sabanis Ying Zhang 0037 Non-asymptotic estimates for TUSLA algorithm for non-convex learning with applications to neural networks with ReLU activation function. 2021 abs/2107.08649 CoRR https://arxiv.org/abs/2107.08649 db/journals/corr/corr2107.html#abs-2107-08649

Pushpendu Ghosh Ariel Neufeld Jajati Keshari Sahoo Forecasting directional movements of stock prices for intraday trading using LSTM and random forests. 2020 abs/2004.10178 CoRR https://arxiv.org/abs/2004.10178 db/journals/corr/corr2004.html#abs-2004-10178

Christian Beck Sebastian Becker Patrick Cheridito Arnulf Jentzen Ariel Neufeld Deep learning based numerical approximation algorithms for stochastic partial differential equations and high-dimensional nonlinear filtering problems. 2020 abs/2012.01194 CoRR https://arxiv.org/abs/2012.01194 db/journals/corr/corr2012.html#abs-2012-01194

Ariel Neufeld Mario Sikic Nonconcave robust optimization with discrete strategies under Knightian uncertainty. 229-253 2019 90 Math. Methods Oper. Res. 2 https://doi.org/10.1007/s00186-019-00669-7 db/journals/mmor/mmor90.html#NeufeldS19

Dominik Alfke Weston Baines Jan Blechschmidt Mauricio J. del Razo Sarmina Amnon Drory Dennis Elbrächter Nando Farchmin Matteo Gambara Silke Glas Philipp Grohs Peter Hinz Danijel Kivaranovic Christian Kümmerle Gitta Kutyniok Sebastian Lunz Jan MacDonald Ryan Malthaner Gregory Naisat Ariel Neufeld Philipp Christian Petersen Rafael Reisenhofer Jun-Da Sheng Laura Thesing Philipp Trunschke Johannes von Lindheim David Weber Melanie Weber 0001 The Oracle of DLphi. 2019 abs/1901.05744 CoRR http://arxiv.org/abs/1901.05744 db/journals/corr/corr1901.html#abs-1901-05744

Christian Beck Sebastian Becker Patrick Cheridito Arnulf Jentzen Ariel Neufeld Deep splitting method for parabolic PDEs. 2019 abs/1907.03452 CoRR http://arxiv.org/abs/1907.03452 db/journals/corr/corr1907.html#abs-1907-03452

Michel Baes Calypso Herrera Ariel Neufeld Pierre Ruyssen Low-Rank plus Sparse Decomposition of Covariance Matrices using Neural Network Parametrization. 2019 abs/1908.00461 CoRR http://arxiv.org/abs/1908.00461 db/journals/corr/corr1908.html#abs-1908-00461

Ariel Neufeld Mario Sikic Robust Utility Maximization in Discrete-Time Markets with Friction. 1912-1937 2018 56 SIAM J. Control. Optim. 3 https://doi.org/10.1137/16M1101829 db/journals/siamco/siamco56.html#NeufeldS18

Dominik Alfke Michel Baes Weston Baines Daniel Bartl Christian Beck Sebastian Becker Jan Blechschmidt Hari Hara Suthan CHari Hara Suthan Chittoor Zeyi Chen Patrick Cheridito Amnon Drory Dennis Elbrächter Matthew Ng Cheng En Matteo Gambara Pushpendu Ghosh Silke Glas Paul Griffin 0001Paul Robert Griffin Philipp Grohs Mile Gu Nando HegemannNando Farchmin Calypso Herrera Peter Hinz Arnulf Jentzen Danijel Kivaranovic Anastasis Kratsios Christian Kümmerle Gitta Kutyniok Mathieu Laurière Yongming Li Luxu Liang Dong-Young Lim Johannes von Lindheim Sebastian Lunz Jan MacDonald Ryan Malthaner Gregory Naisat Ido Nevat Tuan Anh Nguyen Antonis Papapantoleon Kyunghyun Park Philipp PetersenPhilipp Christian Petersen Rafael Reisenhofer Pierre Ruyssen Sotirios Sabanis Jajati Keshari Sahoo Mauricio J. del Razo Sarmina Philipp Schmocker Julian Sester Jun-Da Sheng Shunan Sheng Mario Sikic Laura Thesing Jayne Thompson Viet Khoa Tran Philipp Trunschke David Weber Melanie Weber 0001 Sizhou Wu Qikun Xiang Daiying Yin Ying Zhang Ying Zhang 0037