Physics-Informed Gaussian Process with applications in ODE/PDE parameter estimation

Abstract

<p>Parameter estimation for nonlinear dynamic system models, represented by ordinary differential equations (ODEs) or partial differential equations (PDEs), using noisy and sparse experimental data is a vital task in many fields. We propose a fast and accurate method, physics-informed Gaussian process, for this task. Our method uses a Gaussian process model over system components, explicitly conditioned on the physics information that gradients of the Gaussian process must satisfy the ODE/PDE system. By doing so, we completely bypass the need for numerical integration and achieve substantial savings in computational time. Our method is also suitable for inference with unobserved system components and provides uncertainty quantification. Our method is distinct from existing approaches as we provide a principled statistical construction under a Bayesian framework, which rigorously incorporates the ODE/PDE system through conditioning.</p><p> </p><p>Ref:</p><p> </p><p>PIGP for ODE: <a href="https://www.pnas.org/doi/abs/10.1073/pnas.2020397118">https://www.pnas.org/doi/abs/10.1073/pnas.2020397118</a></p><p>PIGP for PDE: <a href="https://epubs.siam.org/doi/10.1137/22M1514131">https://epubs.siam.org/doi/10.1137/22M1514131</a></p>