for this workshop
Deep learning and partial differential equations
American Institute of Mathematics, San Jose, California
Lin Lin, Jianfeng Lu, and Lexing Ying
The main topics for the workshop are:
- Deep learning for high dimensional PDE problems. Many challenging problems from physical and data sciences (e.g. control theory, molecular dynamics, quantum mechanics) are modeled by PDEs, either of high dimensional functions or with high dimensional parameter fields. Deep neural networks potentially offer a novel and efficient tool for solving these PDE problems.
- PDE and stochastic analysis for deep learning. Though deep learning has brought remarkable empirical successes on many ML/AI problems, traditional statistical learning theories have not been able to explain them. Examples include the effectiveness of the stochastic gradient methods, the generalization power of deep learning, etc. Recently, methods from PDEs and stochastic analysis have provided new perspectives for answering these deep questions.
- PDE and analysis for new architectures. Many successful deep neural network architectures have deep connections with mathematical analysis: CNN with harmonic analysis, RNN and ResNet with ordinary differential equations, etc. The workshop will explore connections between PDE models with new neural network architectures.
This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
Space and funding is available for a few more participants. If you would like to participate, please apply by filling out the on-line form no later than April 14, 2019. Applications are open to all, and we especially encourage women, underrepresented minorities, junior mathematicians, and researchers from primarily undergraduate institutions to apply.
Before submitting an application, please read the description of the AIM style of workshop.
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