GDR Mascot-Num : Workshop on Physics Informed Learning

Contribution List

4. Some statistical insights into PINNs

Nathan DOUMECHE (Sorbonne Université)

12/4/23, 2:00 PM

Physics-informed neural networks (PINNs) combine the expressiveness of neural networks with the interpretability of physical modeling. Their good practical performance has been demonstrated both in the context of solving partial differential equations and in the context of hybrid modeling, which consists of combining an imperfect physical model with noisy observations. However, most of their...

2. Towards instance-dependent approximation guarantees for scientific machine learning using Lipschitz neural networks.

Paul NOVELLO (IRT Saint-Exupéry)

12/4/23, 2:45 PM

Neural networks are increasingly used in scientific computing. Indeed, once trained, they can approximate highly complex, non-linear, and high dimensional functions with significantly reduced computational overhead compared to traditional simulation codes based on finite-differences methods. However, unlike conventional simulation whose error can be controlled, neural networks are statistical,...

6. Physics-informed Gaussian process regression : theory and applications

Iain HENDERSON (Institut de Mathématiques de Toulouse)

12/4/23, 4:15 PM

Gaussian process regression (GPR) is the Bayesian formulation of kernel regression methods used in machine learning. This method may be used to treat regression problems stemming from physical models, the latter typically taking the form of partial differential equations (PDEs).

In this presentation, we study the question of the design of GPR methods, in relation with a target PDE model....

1. Physics-informed polynomial chaos expansion

Lukas NOVAK (Brno University of Technology)

12/4/23, 5:00 PM

Surrogate modeling of costly mathematical models representing physical systems is challenging since it is necessary to fulfill physical constraints in the whole design domain together with specific boundary conditions of investigated systems. Moreover, it is typically not possible to create a large experimental design covering whole input space due to computational burden of original models....

3. Représentation Neural Implicit pour des méthodes numériques hybrides

Emmanuel FRANCK (INRIA)

12/5/23, 9:00 AM

Dans une première partie, nous introduirons les méthodes numériques basées sur des représentations Neural Implicit que sont les PINNs et la méthode Neural Galerkin. Nous tenterons de montrer, que ces méthodes, bien qu'ayant des propriétés bien différentes des méthodes numériques usuelles pour les EDP, restent proche dans l'esprit des méthodes classiques. Après avoir discuté des forces et des...

7. Deep augmented physical models: application to reinforcement learning and computer vision

Vincent LE GUEN (EDF R&D)

12/5/23, 9:45 AM

Modelling and forecasting complex physical systems with only partial knowledge of their dynamics is a major challenge across various scientific fields. Model Based (MB) approaches typically rely on ordinary or partial differential equations (ODE/PDE) and stem from a deep understanding of the underlying physical phenomena. Machine Learning (ML) and deep learning are more prior agnostic and have...

5. Tensor networks and optimal sampling in physics informed machine learning

Philipp TRUNSCHKE (Université de Nantes)

12/5/23, 11:15 AM

Many parametric PDEs have solutions that possess a high degree of regularity with respect to their parameters. Low-rank tensor formats can leverage this regularity to overcome the curse of dimensionality and achieve optimal convergence rates in a wide range of approximation spaces. A particular advantage of these formats is their highly structured nature, which enables us to control the...