Deep learning and partial differential equations

Workshop theme

This workshop will focus on the connections of deep learning and partial differential equations (PDEs). Key topics of this workshop will be:
(i) the design of deep learning-based approximation algorithms for PDEs,

(ii) the rigorous mathematical analysis of such deep learning-based approximation algorithms,

(iii) the performance of such deep learning-based approximation algorithms in the context of high-dimensional PDEs,

(iv) applications, e.g., in optimal control problems, in quantum physics, in nonlinear filtering problems, or in derivative pricing problems, of deep learning-based approximation methods for PDEs, and

(v) the use PDE techniques for studying deep learning-based methodologies.

Due to the ongoing COVID-19 pandemic, all non-UK based applicants should attend this event virtually.

Applications for this workshop are now closed

Fees

Registration Only

Registration Package: £TBC
Student Registration Package: £TBC

The Registration Package includes admission to all seminars, lunches and refreshments on the days that lectures take place (Monday - Friday), wine reception and formal dinner, but does not include other meals or accommodation.

Formal Dinner Only

Formal Dinner: £50

Participants on the Accommodation Package or Registration Package, including organisers and speakers, are automatically included in this event. For all remaining participants who would like to attend, such as programme participants, the above charge will apply.

Accommodation

Unfortunately we do not have any accommodation to offer so all successful applicants will need to source their own accommodation.

Please see the Hotels Combined website for a list of local hotels and guesthouses.

Meals

Lunch Lunch timings and location will be confirmed with timetable.

Evening Meal Participants are free to make their own arrangements for dinner.

Formal Dinner The Formal Dinner location and date is to be confirmed.

Participants on the Accommodation Package or Registration Package, including organisers and speakers, are automatically included in this event.

The Institute kindly requests that any papers published as a result of this programme’s activities are credited as such. Please acknowledge the support of the Institute in your paper using the following text:

The author(s) would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Deep learning and partial differential equations, where work on this paper was undertaken. This work was supported by EPSRC grant EP/R014604/1.

Timetable

Monday 15th November 2021
13:30 to 14:15	Registration	No Room Required
14:15 to 14:30	Christie Marr Isaac Newton Institute Welcome Talk	Room 1
14:30 to 15:00	Justin Sirignano University of Oxford Chair: Karl Kunisch, Moderator Tatiana Alessandra Bubba Deep Learning for the Closure of Partial Differential Equation Models	Room 1
15:00 to 15:30	Stefania Fresca Politecnico di Milano Chair: Karl Kunisch, Moderator Tatiana Alessandra Bubba POD-DL-ROM: a comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs	Room 1
15:30 to 16:00	Afternoon Tea	No Room Required
16:00 to 16:30	Wei Cai Southern Methodist University Chair: Lukas Gonon, Moderator Tatiana Alessandra Bubba Deep neural network algorithms for oscillatory flows and operators, and high dimensional Fokker-Planck equations	Room 1
16:30 to 17:00	Lexing Ying Stanford University Chair: Lukas Gonon, Moderator Tatiana Alessandra Bubba Provably convergent quasistatic dynamics for mean-field two-player zero-sum games	Room 1
17:00 to 18:00	Welcome Wine Reception at INI	No Room Required

Tuesday 16th November 2021
11:10 to 11:30	Morning Coffee	No Room Required
11:30 to 12:00	Ying Peng Shandong University Chair: Philipp Grohs, Moderator Christina Runkel Solving Fully Coupled FBSDEs and Stochastic Hamiltonian Systems via Deep Learning	Room 1
12:00 to 12:30	Christoph Schwab ETH Zürich Chair: Philipp Grohs, Moderator Christina Runkel Deep Learning in High Dimension: Neural Network Approximation of Analytic Functions in $L^2(\mathbb{R}^d)$	Room 1
12:30 to 13:30	Lunch and Poster Session	No Room Required
13:30 to 14:30	Poster Session	Room 1
14:30 to 15:00	Lisa Maria Kreusser University of Cambridge; Bath Institute for Mathematical Innovation Chair: Ruimeng Hu, Moderator Christina Runkel On anisotropic diffusion equations for label propagation	Room 1
15:00 to 15:30	Stephan Wojtowytsch Texas A&M University Chair: Ruimeng Hu, Moderator Christina Runkel On the solution of partial differential equations in spaces of neural networks	Room 1
15:30 to 15:35	Group Photo	No Room Required
15:35 to 16:00	Afternoon Tea	No Room Required
16:00 to 16:30	Lars Ruthotto Emory University Chair: Justin Sirignano, Moderator Christina Runkel A Machine Learning Framework for High-Dimensional Mean Field Games and Optimal Control	Room 1
16:30 to 17:00	Wei Kang Naval Postgraduate School Chair: Justin Sirignano, Moderator Christina Runkel Compositional Features and Feedforward Neural Networks for High Dimensional Problems	Room 1

Wednesday 17th November 2021
10:30 to 11:00	Bin Dong Peking University Chair: Patrick Cheridito, Moderator Subhadip Mukherjee Learning and Learning to Solve PDEs	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:00	Siddhartha Mishra ETH Zurich Chair: Patrick Cheridito, Moderator Subhadip Mukherjee On Physics Informed Neural Networks (PINNs) for approximating PDEs	Room 1
12:00 to 12:30	Dante Kalise Imperial College London Chair: Patrick Cheridito, Moderator Subhadip Mukherjee Gradient-augmented supervised learning of feedback control laws for high-dimensional nonlinear dynamics	Room 1
12:30 to 13:30	Lunch	No Room Required
13:30 to 15:30	Free Afternoon	No Room Required
15:30 to 16:00	Afternoon Tea	No Room Required
16:00 to 16:30	Ruimeng Hu University of California, Santa Barbara Chair: Stephan J. Wojtowytsch, Moderator Subhadip Mukherjee Convergence of Empirical Measures, Mean-Field Games and Signatures	Room 1
16:30 to 17:00	George Karniadakis Brown University Chair: Stephan J. Wojtowytsch, Moderator Subhadip Mukherjee TBA	Room 1
19:30 to 22:00	Formal Dinner	No Room Required

Thursday 18th November 2021
12:30 to 13:30	Lunch	No Room Required
13:30 to 14:00	Break	No Room Required
14:00 to 14:30	Patrick Cheridito ETH Zürich Chair: Lisa Maria Kreusser, Moderator Sören Dittmer Deep splitting method for (S)PDEs	Room 1
14:30 to 15:00	David Pardo University of the Basque Country; BCAM - Basque Center for Applied Mathematics Chair: Lisa Maria Kreusser, Moderator Sören Dittmer A Deep Ritz method with r-adaptivity for solving Partial Differential Equations	Room 1
15:00 to 15:30	Lukas Gonon Ludwig-Maximilians-Universität München Chair: Lisa Maria Kreusser, Moderator Sören Dittmer Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality	Room 1
15:30 to 16:00	Afternoon Tea	No Room Required
16:00 to 16:30	Jianfeng Lu Duke University Chair: Sid Mishra, Moderator Sören Dittmer A Priori Error Analysis for Solving High Dimensional Elliptic PDEs Based on Neural Networks	Room 1
16:30 to 17:00	Jiequn Han Princeton University Chair: Sid Mishra, Moderator Sören Dittmer Learning Nonlocal Constitutive PDE Models with Vector-Cloud Neural Networks	Room 1

Friday 19th November 2021
12:30 to 13:30	Lunch	No Room Required
13:30 to 14:00	Break	No Room Required
14:00 to 14:30	Karl Kunisch University of Graz Chair: Jiequn Han, Moderator Ferdia Sherry Feedback stabilization of Autonomous Systems via Deep Neural Network Approximation	Room 1
14:30 to 15:00	Andrea Manzoni Politecnico di Milano Chair: Jiequn Han, Moderator Ferdia Sherry Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based ROMs	Room 1
15:00 to 15:30	Sebastian Peitz Universität Paderborn Chair: Jiequn Han, Moderator Ferdia Sherry On the Universal Transformation of Data-Driven Models to Control Systems	Room 1
15:30 to 16:00	Afternoon Tea	No Room Required

Deep learning and partial differential equations

Organisers

Weinan E Princeton University
Philipp Grohs University of Vienna; Austrian Academy of Sciences
Arnulf Jentzen Universität Münster; Chinese University of Hong Kong
Gitta Kutyniok Technische Universität Berlin

Speakers

Wei Cai Southern Methodist University
Patrick Cheridito ETH Zürich
Bin Dong Peking University
Stefania Fresca Politecnico di Milano
Lukas Gonon Ludwig-Maximilians-Universität München
Jiequn Han Princeton University
Ruimeng Hu University of California, Santa Barbara
Dante Kalise Imperial College London
Wei Kang Naval Postgraduate School
George Karniadakis Brown University
Lisa Maria Kreusser University of Cambridge; Bath Institute for Mathematical Innovation
Karl Kunisch University of Graz
Jianfeng Lu Duke University
Andrea Manzoni Politecnico di Milano
Christie Marr Isaac Newton Institute
Siddhartha Mishra ETH Zurich
David Pardo University of the Basque Country; BCAM - Basque Center for Applied Mathematics
Sebastian Peitz Universität Paderborn
Ying Peng Shandong University
Lars Ruthotto Emory University
Christoph Schwab ETH Zürich
Justin Sirignano University of Oxford
Stephan Wojtowytsch Texas A&M University
Lexing Ying Stanford University

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