Data-Driven Discovery of Conservation Laws from Trajectories via Neural Deflation

In an earlier work by a subset of the present authors, the method of the so-called neural deflation was introduced towards identifying a complete set of functionally independent conservation laws of a nonlinear dynamical system. Here, we extend by a significant step this proposal. Instead of using the explicit knowledge of the underlying equations of motion, we develop the method directly from system trajectories. This is crucial towards enhancing the practical implementation of the method in scenarios where solely data reflecting discrete snapshots of the system are available. We showcase the results of the method and the number of associated conservation laws obtained in a diverse range of examples including 1D and 2D harmonic oscillators, the Toda lattice, the Fermi-Pasta-Ulam-Tsingou lattice and the Calogero-Moser system.

A Modified PINN Approach for Identifiable Compartmental Models in Epidemiology with Applications to COVID-19

A variety of approaches using compartmental models have been used to study the COVID-19 pandemic and the usage of machine learning methods with these models has had particularly notable success. We present here an approach toward analyzing accessible data on Covid-19's U.S. development using a variation of the "Physics Informed Neural Networks" (PINN) which is capable of using the knowledge of the model to aid learning. We illustrate the challenges of using the standard PINN approach, then how with appropriate and novel modifications to the loss function the network can perform well even in our case of incomplete information. Aspects of identifiability of the model parameters are also assessed, as well as methods of denoising available data using a wavelet transform. Finally, we discuss the capability of the neural network methodology to work with models of varying parameter values, as well as a concrete application in estimating how effectively cases are being tested for in a population, providing a ranking of U.S. states by means of their respective testing.