Speaker
Description
A common inverse problem in systems biology, biophysics and related disciplines is the inference of model parameters from limited measured data. For cases where the underlying dynamics follow a set of known (or assumed) differential equations, Physics-Informed Neural Networks (PINNs) have been put forward as decent approximators of the inverse equations, offering an alternative way to estimate parameters to classical methods. However, naive application of PINNs for parameter inference suffers from uncontrolled overfitting and convergence problems when the available data is noisy. Here we show that these problems stem from inadequate loss function design and training. We introduce PINNverse, a recently proposed reinterpretation of the PINN training paradigm as a constrained optimization problem, which overcomes these limitations. PINNverse combines the advantages of PINNs with the Modified Differential Method of Multipliers and enables convergence to any point on the Pareto front. Based on a few classical ODE and PDE problems, we demonstrate that PINNverse accurately infers model parameters even under high levels of noise in sparse data. Finally, some potential future applications are discussed.
