Path sampling of recurrent neural networks by incorporating known physics

Abstract

Recurrent neural networks have seen widespread use in modeling dynamical systems in varied domains such as weather prediction, text prediction and several others. Often one wishes to supplement the experimentally observed dynamics with prior knowledge or intuition about the system. While the recurrent nature of these networks allows them to model arbitrarily long memories in the time series used in training, it makes it harder to impose prior knowledge or intuition through generic constraints. In this work, we present a path sampling approach based on principle of Maximum Caliber that allows us to include generic thermodynamic or kinetic constraints into recurrent neural networks. We show the method here for a widely used type of recurrent neural network known as long short-term memory network in the context of supplementing time series collecting from all-atom molecular dynamics. We demonstrate the power of the formalism for different applications. Our method can be easily generalized to other generative artificial intelligence models and to generic time series in different areas of physical and social sciences, where one wishes to supplement limited data with intuition or theory based corrections.

A comparative study of different machine learning methods for dissipative quantum dynamics

“…Recently, many ML models have been applied to simulate the dynamics of quantum systems [32][33][34][35][119][120][121][122][123][124][125][126][127][128]. We note that ML can also be applied to quantum dynamics in a different context-namely as surrogate models for quantum chemical properties such as potential energies and forces in different electronic states as well as couplings between the states eliminating the need for expensive (excited-state) electronic structure calculations [129][130][131].…”

A comparative study of different machine learning methods for dissipative quantum dynamics

“…Recently, many ML models have been applied to simulate the dynamics of quantum systems. [32][33][34][35][117][118][119][120][121][122][123][124][125][126] We note that ML can also be applied to quantum dynamics in a different context-namely as surrogate models for quantum chemical properties such as potential energies and forces in different electronic states as well as cou-plings between states eliminating the need for expensive (excited-state) electronic structure calculations. [127][128][129] Here we apply ML to propagate a quantum system assuming potential energies are readily available.…”

A comparative study of different machine learning methods for dissipative quantum dynamics

“…116 Recently, many ML models have been applied to simulate the dynamics of quantum systems. [32][33][34][35][117][118][119][120][121][122][123][124][125][126] We note that ML can also be applied to quantum dynamics in a different context-namely as surrogate models for quantum chemical properties such as potential energies and forces in different electronic states as well as couplings between the states eliminating the need for expensive (excited-state) electronic structure calculations. [127][128][129] Here we apply ML to propagate a quantum system assuming potential energies are readily available.…”