Quantification of total uncertainty in the physics-informed reconstruction of CVSim-6 physiology.

When predicting physical phenomena through simulation, quantification of the total uncertainty due to multiple sources is as crucial as making sure the underlying numerical model is accurate. Possible sources include irreducible uncertainty due to noise in the data, uncertainty induced by insufficient data or inadequate parameterization, and uncertainty related to the use of misspecified model equations. In addition, recently proposed approaches provide flexible ways to combine information from data with full or partial satisfaction of equations that typically encode physical principles.

AI-Aristotle: A physics-informed framework for systems biology gray-box identification.

Discovering mathematical equations that govern physical and biological systems from observed data is a fundamental challenge in scientific research. We present a new physics-informed framework for parameter estimation and missing physics identification (gray-box) in the field of Systems Biology. The proposed framework-named AI-Aristotle-combines the eXtreme Theory of Functional Connections (X-TFC) domain-decomposition and Physics-Informed Neural Networks (PINNs) with symbolic regression (SR) techniques for parameter discovery and gray-box identification.

Physics-informed neural networks and functional interpolation for stiff chemical kinetics.

This work presents a recently developed approach based on physics-informed neural networks (PINNs) for the solution of initial value problems (IVPs), focusing on stiff chemical kinetic problems with governing equations of stiff ordinary differential equations (ODEs). The framework developed by the authors combines PINNs with the theory of functional connections and extreme learning machines in the so-called extreme theory of functional connections (X-TFC). While regular PINN methodologies appear to fail in solving stiff systems of ODEs easily, we show how our method, with a single-layer neural network (NN) is efficient and robust to solve such challenging problems without using artifacts to reduce the stiffness of problems.