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. We test the accuracy, speed, flexibility, and robustness of AI-Aristotle based on two benchmark problems in Systems Biology: a pharmacokinetics drug absorption model and an ultradian endocrine model for glucose-insulin interactions. We compare the two machine learning methods (X-TFC and PINNs), and moreover, we employ two different symbolic regression techniques to cross-verify our results. To test the performance of AI-Aristotle, we use sparse synthetic data perturbed by uniformly distributed noise. More broadly, our work provides insights into the accuracy, cost, scalability, and robustness of integrating neural networks with symbolic regressors, offering a comprehensive guide for researchers tackling gray-box identification challenges in complex dynamical systems in biomedicine and beyond.

Waves at a fluid-solid interface: Explicit versus implicit formulation of boundary conditions using a discontinuous Galerkin method.

An accurate solution of the wave equation at a fluid-solid interface requires a correct implementation of the boundary condition. Boundary conditions at fluid-solid interface require continuity of the normal component of particle velocity and traction, whereas the tangential components vanish. A main challenge is to model interface waves, namely, the Scholte and leaky Rayleigh waves. This study uses a nodal discontinuous Galerkin (dG) finite-element method with the medium discretized using an unstructured uniform triangular meshes. The natural boundary conditions in the dG method are implemented by (1) using an explicit upwind numerical flux and (2) by using an implicit penalty flux and setting the modulus of rigidity of the acoustic medium to zero. The accuracy of these methods is evaluated by comparing the numerical solutions with analytical ones, with source and receiver at and away from the interface. The study shows that the solutions obtained from the explicit and implicit boundary conditions provide the correct results. The stability of the dG scheme is determined by the numerical flux, which also implements the boundary conditions by unifying the numerical solution at shared edges of the elements in an energy stable manner.