Machine learning methods based on data, physical laws, or their combination have emerged recently as alternatives to classical numerical methods for physical systems modeling. When the governing PDEs are known, physics-informed learning approaches can solve these PDEs (forward problems). They can also infer unknown parameters, or identify missing functionals in constitutive relations (inverse problems).

However, these approaches face several challenges, such as training difficulties, long-time integration, large-scale domains, and multi-scale and multi-physics aspects. This mini-symposium aims to discuss recent advances in both the methodological and application aspects of data-driven and physics-based approaches.

We welcome contributions on machine learning methods for parametric time-dependent problems, including data-driven approaches, PINNs, Neural-Operators, stochastic methods, diffusion methods, and more. Applications may cover a wide range of computational mechanics.