Dynamical processes are abundant in science and engineering, and understanding them is crucial for discovery and design. With growing availability of high-throughput experimental and computational data, learning or simplifying dynamical models of physical processes from observational data is an increasingly important task. In this line of work, we are interested in developing principled deep learning methodologies for accelerating scientific discovery in problems involving dynamical systems.
Directions include
- Learning, reducing and controlling dynamics
- Accelerating scientific computing
- Data-driven multiscale modelling
- Data-driven analysis of rare events
- Data-driven inverse problems
- Koopman operator analysis of dynamical systems
Papers
[1] A. Zhu and Q. Li, ‘DynGMA: A robust approach for learning stochastic differential equations from data’, Journal of Computational Physics, vol. 513, p. 113200, Sep. 2024, doi: 10.1016/j.jcp.2024.113200.
[2] S. Arisaka and Q. Li, ‘Accelerating Legacy Numerical Solvers by Non-intrusive Gradient-based Meta-solving’, in Proceedings of the 41th International Conference on Machine Learning, PMLR, Jul. 2024.
[3] D. T. Doncevic et al., ‘A Recursively Recurrent Neural Network (R2N2) Architecture for Learning Iterative Algorithms’, SIAM J. Sci. Comput., vol. 46, no. 2, pp. A719–A743, Apr. 2024, doi: 10.1137/22M1535310.
[4] S. Wu, L. Chamoin, and Q. Li, ‘Non-intrusive model combination for learning dynamical systems’, Physica D: Nonlinear Phenomena, p. 134152, Apr. 2024, doi: 10.1016/j.physd.2024.134152.
[5] X. Chen et al., ‘Constructing custom thermodynamics using deep learning’, Nature Computational Science, vol. 4, no. 1, pp. 66–85, 2024.
[6] S. Arisaka and Q. Li, ‘Principled Acceleration of Iterative Numerical Methods Using Machine Learning’, in Proceedings of the 40th International Conference on Machine Learning, PMLR, Jul. 2023, pp. 1041–1059. Accessed: Aug. 09, 2023. [Online]. Available: https://proceedings.mlr.press/v202/arisaka23a.html
[7] M. Zhang, Q. Li, and J. Liu, ‘On stability and regularization for data-driven solution of parabolic inverse source problems’, Journal of Computational Physics, vol. 474, p. 111769, Feb. 2023, doi: 10.1016/j.jcp.2022.111769.
[8] B. Lin, Q. Li, and W. Ren, ‘Computing high-dimensional invariant distributions from noisy data’, Journal of Computational Physics, vol. 474, p. 111783, Feb. 2023, doi: 10.1016/j.jcp.2022.111783.
[9] K. Hippalgaonkar, Q. Li, X. Wang, J. W. Fisher, J. Kirkpatrick, and T. Buonassisi, ‘Knowledge-integrated machine learning for materials: lessons from gameplaying and robotics’, Nat Rev Mater, pp. 1–20, Jan. 2023, doi: 10.1038/s41578-022-00513-1.
[10] H. P. Anwar Ali, Z. Zhao, Y. J. Tan, W. Yao, Q. Li, and B. C. K. Tee, ‘Dynamic Modeling of Intrinsic Self-Healing Polymers Using Deep Learning’, ACS Appl. Mater. Interfaces, vol. 14, no. 46, pp. 52486–52498, Nov. 2022, doi: 10.1021/acsami.2c14543.
[11] Z. Zhao and Q. Li, ‘Adaptive sampling methods for learning dynamical systems’, in Proceedings of Mathematical and Scientific Machine Learning, PMLR, Sep. 2022, pp. 335–350. Accessed: Jan. 07, 2023. [Online]. Available: https://proceedings.mlr.press/v190/zhao22a.html
[12] Y. Guo et al., ‘Personalized Algorithm Generation: A Case Study in Learning ODE Integrators’, SIAM J. Sci. Comput., pp. A1911–A1933, Aug. 2022, doi: 10.1137/21M1418629.
[13] B. Lin, Q. Li, and W. Ren, ‘Computing the Invariant Distribution of Randomly Perturbed Dynamical Systems Using Deep Learning’, Journal of Scientific Computing, vol. 91, no. 3, p. 77, May 2022, doi: 10.1007/s10915-022-01844-5.
[14] B. Lin, Q. Li, and W. Ren, ‘A Data Driven Method for Computing Quasipotentials’, in Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference, PMLR, Apr. 2022, pp. 652–670. [Online]. Available: https://proceedings.mlr.press/v145/lin22b.html
[15] H. Yu, X. Tian, W. E, and Q. Li, ‘OnsagerNet: Learning stable and interpretable dynamics using a generalized Onsager principle’, Phys. Rev. Fluids, vol. 6, no. 11, p. 114402, Nov. 2021, doi: 10.1103/PhysRevFluids.6.114402.
[16] F. Mekki-Berrada et al., ‘Two-step machine learning enables optimized nanoparticle synthesis’, npj Computational Materials, vol. 7, no. 1, p. 55, Apr. 2021, doi: 10.1038/s41524-021-00520-w.
[17] D. Bash et al., ‘Multi-Fidelity High-Throughput Optimization of Electrical Conductivity in P3HT-CNT Composites’, Advanced Functional Materials, vol. 31, no. 36, p. 2102606, 2021, doi: 10.1002/adfm.202102606.
[18] Q. Li, B. Lin, and W. Ren, ‘Computing committor functions for the study of rare events using deep learning’, The Journal of Chemical Physics, vol. 151, no. 5, p. 054112, Aug. 2019, doi: 10.1063/1.5110439.
[19] J. N. Kumar, Q. Li, K. Y. T. Tang, T. Buonassisi, A. L. Gonzalez-Oyarce, and J. Ye, ‘Machine learning enables polymer cloud-point engineering via inverse design’, npj Computational Materials, vol. 5, no. 1, p. 73, 2019, doi: 10.1038/s41524-019-0209-9.
[20] E. M. Bollt, Q. Li, F. Dietrich, and I. Kevrekidis, ‘On matching, and even rectifying, dynamical systems through Koopman operator eigenfunctions’, SIAM Journal on Applied Dynamical Systems, vol. 17, no. 2, pp. 1925–1960, 2018.
[21] Q. Li, F. Dietrich, E. M. Bollt, and I. G. Kevrekidis, ‘Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator’, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 27, no. 10, p. 103111, 2017.
Slides
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