News & Highlights
The The AI Scientist - Physics Informed Neural Networks (PINNs) has been published online as part of the NeurIPS 2025 Education Program!
This program received submissions from educators worldwide, and I am delighted that this contribution has been selected. The material is designed specifically for school students, requiring no prior knowledge of advanced AI concepts, in line with the program’s mission to make AI accessible to learners of all levels.
M. Kumar, The AI Scientist - Physics Informed Neural Networks (PINNs), NeurIPS 2025 Education Program.
Neural ODEs model transformations in a continuous-depth framework, enabling applications that range from image generation and sequence modeling to scientific computing. Despite their success, a key open question has persisted: How well do Neural ODEs generalize to unseen data?
Our work accepted in TMLR, developed a generalization bound for Neural ODEs with nonlinear and time-dependent dynamics, assuming only that the underlying function is Lipschitz continuous. By advancing the theoretical understanding of Neural ODEs, we move closer to explaining why these continuous-depth models can learn effectively across diverse domains.
M. Kumar, M. Verma, Analysis of generalization capacities of Neural Ordinary Differential Equations, 2025, Transactions on Machine Learning Research.
Our study, accepted in Scientific Reports, introduces a novel temperature and altitude-dependent SIR-SI model for malaria transmission. We integrate physics-informed neural networks (PINNs) for parameter inference and use Dynamic Mode Decomposition (DMD) to develop a real-time transmission risk index, offering a data-driven yet interpretable framework for predictive modeling and intervention planning.
A. Rajnarayanan, M. Kumar, A. Tridane, Analysis of a mathematical model for malaria using data-driven approach, 2025, Scientific Reports.