Bayesian Deep Learning for Partial Differential Equation Parameter Discovery with Sparse and Noisy Data

Understand

Scientific machine learning has been successfully applied to inverse problems and PDE discovery in computational physics.

• One caveat concerning current methods is the need for large amounts of ("clean") data, in order to characterize the full system response and discover underlying physical models.
• Bayesian methods may be particularly promising for overcoming these challenges, as they are naturally less sensitive to the negative effects of sparse and noisy data.
• In this paper, we propose to use Bayesian neural networks (BNN) in order to: 1) Recover the full system states from measurement data (e.g.