Invited talk

Slides:

1. Opportunities and Challenges of Neural Networks for Partial Differential Equations.

2. Superconvergence Approximation and Optimal Generalization Analysis of Deep Neural Networks for Solving Partial Differential Equations.

3. Statistical Learning Guarantees for Group-Invariant Barron Functions.

38. 4th Southeast Applied & Computational Math Student Workshop (Emory University), April 3-4, 2026. Learning in Group-Invariant Radon Spaces from Finite Samples. 

37. SIAM Conference on Uncertainty Quantification (UQ26), Mar. 22–25, 2026. Statistical Learning Guarantees for Group-Invariant Barron Functions.

36. Computational and Applied Math Seminar (Tufts University), Mar. 2, 2026. Opportunities and Challenges of Neural Networks for Partial Differential Equations.

35. Mathematical Sciences Colloquium (Rensselaer Polytechnic Institute), Feb. 25, 2026. Opportunities and Challenges of Neural Networks for Partial Differential Equations.

34. Analysis and Data Science Seminar (University at Albany), Feb. 24, 2026. Superconvergence Approximation and Optimal Generalization Analysis of Deep Neural Networks for Solving Partial Differential Equations.

33. Special Mathematics Colloquium (Case Western Reserve University), Jan. 20, 2026. Opportunities and Challenges of Neural Networks in Partial Differential Equations.

32. Special Mathematics Colloquium (University of Kentucky), Jan. 16, 2026. Opportunities and Challenges of Neural Networks in Partial Differential Equations.

31. Special Mathematics Colloquium (Rowan University), Dec. 12, 2025. Opportunities and Challenges of Neural Networks in Partial Differential Equations.

30. Special Mathematics Colloquium (Binghamton University), Dec. 10, 2025. Opportunities and Challenges of Neural Networks in Partial Differential Equations.

29. Short Course and Workshop on Scientific Machine Learning and Applications, Dec. 25, 2025–Jan. 6, 2026 (University of Hawaiʻi at Mānoa). Opportunities and Challenges of Neural Networks in Partial Differential Equations (Workshop); Optimal Error Estimates for Deep Neural Networks with the Curse of Dimensionality (Short Courses).

28. Deep learning theory seminar, Nov. 7, 2025. Nearly Optimal VC-Dimension and Pseudo-Dimension Bounds for Deep Neural Network Derivatives.

27. SIAM-NNP Conference 2025, Nov. 2, 2025 (Penn State). Deep Neural Networks with General Activations: Super-Convergence in Sobolev Norms.

26. SIAM-NNP Conference 2025, Nov. 1, 2025 (Penn State). Multiscale Neural Networks for Approximating Green’s Functions.

25. Department of Mathematics (Emory University), Oct. 2, 2025. Opportunities and Challenges of Neural Networks in Partial Differential Equations.

24. Seminar Talk, School of Mathematics (Fudan University), May 22, 2025. Optimal Approximation and Generalization Analysis for Deep Neural Networks for Solving Partial Differential Equation.

23. Seminar Talk, School of Mathematics (Xiamen University), May 21, 2025. Homotopy Dynamics for Neural Networks in Solving Partial Differential Equations.

22. Seminar Talk, School of Science and Engineering (CUHK Shenzhen), May 20, 2025. Optimal Approximation and Generalization Analysis for Deep Neural Networks for Solving Partial Differential Equations.

21. Seminar Talk, Research Center for Mathematics (BNU-UIC), May 19, 2025. Homotopy Dynamics for Neural Networks in Solving Partial Differential Equations.

20. Frontiers in Applied Modeling and Scientific Computing (UM), May 15, 2025. Homotopy Dynamics for Neural Networks in Solving Partial Differential Equations.

19. Department of Mathematics Colloquium (HKBU), May 14, 2025. Operator Learning for solving linear and nonlinear partial differential equations.

18. Seminar on Applied Mathematics (HKUST), May 12, 2025. Homotopy Dynamics for Neural Networks in Solving Partial Differential Equations.

17. Applied and Computational Mathematics Seminar (Georgia Tech), Apr. 14, 2025. Approximation and Generalization Analysis for Deep Neural Networks for Solving Partial Differential Equations to Achieve Super-convergence Rate.

16. Brownbag Seminar (CMSE, MSU), Apr. 3, 2025. Operator Learning for solving linear and nonlinear partial differential equations.

15. Special Mathematics Colloquium, Department of Mathematical Sciences, KAUST, Mar. 2, 2025. Enhancing Neural Network Training for Complex PDEs: Algorithms, Architectures, and Integration with Traditional Methods.

14. Special Mathematics Colloquium, Department of Mathematical Sciences, University of Delaware, Jan. 10, 2025. Enhancing Neural Network Training for Complex PDEs: Algorithms, Architectures, and Integration with Traditional Methods.

13. NeurIPS 2024, Dec. 9–15, 2024. Newton Informed Neural Operator for Computing Multiple Solutions of Nonlinear Partial Differential Equations.

12. 2024 SIAM New York–New Jersey–Pennsylvania Section Conference, Nov. 1–3, 2024. Newton Informed Neural Operator for Computing Multiple Solutions of Nonlinear Partial Differential Equations.

11. Special Mathematics Colloquium (UTK), Oct. 30, 2024. Approximation, Generalization, and Training Error in Solving Partial Differential Equations with Deep Neural Networks.

10. SIAM Conference on Data Science, Oct. 21–25, 2024. Newton Informed Neural Operator for Computing Multiple Solutions of Nonlinear Partial Differential Equations.

9. Mathematical Biosciences Workshop, Aug. 8–9, 2024. On pattern formation in the thermodynamically-consistent variational Gray–Scott model.

8. ICML 2024, Jul. 21–27, 2024. Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Loss.

7. The 17th SIAM East Asian Section Conference, Jun. 30, 2024. Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Loss.

6. CSE–Math Seminars (UMN), Apr. 22, 2024. Approximation and Generalization Errors in Deep Neural Networks for Sobolev Spaces measured by Sobolev Norms.

5. Scientific Computing and Machine Learning Seminar (KAUST), Feb. 14, 2024. Approximation and Generalization Errors in Deep Neural Networks for Sobolev Spaces measured by Sobolev Norms.

4. NeurIPS 2023, Dec. 10–16, 2023. Nearly Optimal VC-Dimension and Pseudo-Dimension Bounds for Deep Neural Network Derivatives.

3. SIAM-NNP Conference 2023, Oct. 20–22, 2023 (NJIT). Homotopy Relaxation Training Algorithms for Infinite-Width Two-Layer ReLU Neural Networks.

2. EASIAM Workshop on Applied and Computational Mathematics, May 17–19, 2023. Approximation of Functionals by Neural Network without Curse of Dimensionality.

1...SIAM Conference on Mathematical Aspects of Materials Science (online), May 17–28, 2021. Convergence from Atomistic Model to Peierls–Nabarro Model for Dislocations in Bilayer System with Complex Lattice.