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Computing Nonequilibrium Responses with Score-Shifted Stochastic Differential Equations
Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic dynamics. For nonequilibrium systems, perturbations cannot be interpreted simply by monitoring fluctuations in a conjugate observable and general response results rely on path ensemble averaging. Furthermore, these techniques do not apply to perturbations that affect the diffusion tensor in a stochastic system. Here, we introduce an “effective” physical process that represents the diffusion perturbed dynamics and enables accurate calculations of responses to a change in the diffusion. Interestingly, the effective dynamics contain an additional drift involving the instantaneous “score” of the system, and we leverage score matching algorithms to carry out nonequilibrium response calculations on systems for which the exact stationary distribution is unknown.
Resummation of the Holstein-Primakoff expansion and differential equation approach to operator square roots
Not Available
The Differential Equations That Model Diseases
In this brief tutorial, I will describe the simplest way of modeling a deadly infectious disease, such as COVID-19. I will show that at early times, the disease grows exponentially, but at late times, falls off like a Bell curve. I will solve the equations numerically with Python. A common mathematical model is the so-called compartmental model, where diseases can move people between "categories" such as healthy, infectious, or truly sick. This is a large, well established field and there are many good resources on this topic. I started with the SIAM review article The mathematics of infectious diseases. However, there are many excellent textbooks and more modern reviews as well.
The Mallat Scattering Transform fro reduced order modeling of partial differential equations.
Abstract not provided.
Connecting Functions of Nonlinear Ordinary Differential Equations.
Abstract not provided.
Assessing the Efficacy of Universal Differential Equations to Learn Missing Dynamics from a Subset of Observable State Variables.
Abstract not provided.
Data-Driven Model-Form Uncertainty with Bayesian Statistics and Neural Differential Equations.
Abstract not provided.
Efficient Simulation of Stiff Stochastic Differential Equations.
Abstract not provided.
Data-Driven Model-Form Uncertainty with Bayesian Statistics and Neural Differential Equations.
Abstract not provided.
Mesh Optimization and Basis Compression]{Mesh Optimization and Basis Compression for Extreme-Scale Solution of Partial Differential Equations
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Neural Universal Differential Equation Hypernetwork Surrogates for Agent-Based Disease Models
Presentation for SIAM CSE 2025 on new surrogate modeling for epidemiological agent-based models
Basis Compression for Extreme-Scale Solution of Partial Differential Equations
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