Research-SciML

Scientific Machine Learning

Scientific machine learning (SciML) may be understood as an inquiry into the conditions under which scientific knowledge is possible in data-rich regimes of complex systems. Rather than treating data as passive observations, it regards them as constitutive elements that shape the formation and justification of scientific representations. In this framework, learning is not an auxiliary computational tool, but a principle mean of organizing high-dimensional complexity into structures that admit interpretation and prediction. SciML therefore defines a mode of inquiry in which data, representation, and understanding are mutually conditioned, allowing complex, nonlinear, and multiscale phenomena to be rendered intelligible.

PAS-NetPAS-Net is a new operator-learning architecture that we developed to address a fundamental challenge in scientific machine learning: how to reliably learn nonlinear PDE solution operators that exhibit multiscale structure, sharp layers, stiff dynamics, and small-parameter effects. This framework extends PI-DeepONet by introducing a locally adaptive rescaling of spatial coordinates inside the trunk network, creating a built-in multiscale feature embedding that significantly enhances the network’s expressive power. The resulting representation acts as an architecture-independent preconditioner, improving the conditioning of the underlying Neural Tangent Kernel (NTK) and yielding faster, more stable convergence during training.
Ref. Mou, C., Zhang, Y., Zhu, X., & Zhuang, Q. (2025). PAS-Net: Physics Informed Adaptive Scale Deep Operator Learning. Submitted; preprint, arXiv:2511.14925.

Neural-PODNeural-POD is a neural operator framework I developed to generalize the classical Proper Orthogonal Decomposition (POD) beyond linear SVD-based approximations. Instead of extracting modes through eigen-decompositions, Neural-POD constructs basis functions through a sequence of neural residual minimization problems, mirroring a nonlinear, data-driven version of Gram–Schmidt orthogonalization.
Ref. Mou, C., Lu, B., & Lin, G. (2025). Neural-POD: A Neural Operator Approach for Infinite-Dimensional Functional Proper Orthogonal Decomposition. To be submitted.

MoPINNEnKF MoPINNEnKF is an integrated framework that combines Physics-Informed Neural Networks (PINNs), the Non-Dominated Sorting Genetic Algorithm III (NSGA-III), and the Ensemble Kalman Filter (EnKF) to solve forward and inverse PDE problems under noisy or incomplete data conditions. NSGA-III generates diverse PINN ensembles along the Pareto front to balance multi-objective losses, while EnKF assimilates noisy observations to iteratively refine these models. This synergy enhances robustness, accuracy, and uncertainty quantification, significantly outperforming standard PINNs in handling noise and missing physics.
Ref. Lu, B.†, Mou, C., & Lin, G. (2025). iPINNER: An Iterative Physics-Informed Neural Network with Ensemble Kalman Filter. Journal of Computational Physics, 114592.

EvoKANEvoKAN is a neural-operator framework that couples Kolmogorov–Arnold Networks (KANs) with an evolutionary learning strategy to solve complex PDEs. The network parameters evolve under the governing equations, enabling long-term prediction without retraining. With the Scalar Auxiliary Variable (SAV) method, EvoKAN ensures energy stability and high computational efficiency, accurately capturing multiscale dynamics in problems such as the Allen–Cahn and Navier–Stokes equations.
Ref. Lin, G., Mou, C., & Zhang, J. (2025). Energy-dissipative evolutionary kolmogorov-arnold networks for complex pde systems. arXiv preprint arXiv:2503.01618.

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