Related papers: Partial observations and conservation laws: Grey-b…

In this paper, a general framework for the analysis of a connection between the training of artificial neural networks via the dynamics of Markov chains and the approximation of conservation law equations is proposed. This framework allows…

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…

Conservation laws are an inherent feature in many systems modeling real world phenomena, in particular, those modeling biological and chemical systems. If the form of the underlying dynamical system is known, linear algebra and algebraic…

Multiscale systems are ubiquitous in science and technology, but are notoriously challenging to simulate as short spatiotemporal scales must be appropriately linked to emergent bulk physics. When expensive high-dimensional dynamical systems…

Many software engineering tasks, such as testing, and anomaly detection can benefit from the ability to infer a behavioral model of the software.Most existing inference approaches assume access to code to collect execution sequences. In…

One of the major challenges in biology concerns the integration of data across length and time scales into a consistent framework: how do macroscopic properties and functionalities arise from the molecular regulatory networks - and how can…

Inferring behavior model of a running software system is quite useful for several automated software engineering tasks, such as program comprehension, anomaly detection, and testing. Most existing dynamic model inference techniques are…

This paper addresses the data-driven identification of latent dynamical representations of partially-observed systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications,…

Data-driven fault diagnosis is complicated by unknown fault classes and limited training data from different fault realizations. In these situations, conventional multi-class classification approaches are not suitable for fault diagnosis.…

This paper presents an energy-preserving machine learning method for inferring reduced-order models (ROMs) by exploiting the multi-symplectic form of partial differential equations (PDEs). The vast majority of energy-preserving…

We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a…

How can we find interpretable, domain-appropriate models of natural phenomena given some complex, raw data such as images? Can we use such models to derive scientific insight from the data? In this paper, we propose some methods for…

We consider the application of deep generative models in propagating uncertainty through complex physical systems. Specifically, we put forth an implicit variational inference formulation that constrains the generative model output to…

Deep learning algorithms have recently shown to be a successful tool in estimating parameters of statistical models for which simulation is easy, but likelihood computation is challenging. But the success of these approaches depends on…

Simulation of the dynamics of physical systems is essential to the development of both science and engineering. Recently there is an increasing interest in learning to simulate the dynamics of physical systems using neural networks.…

This article considers the generative modeling of the (mixed) states of quantum systems, and an approach based on denoising diffusion model is proposed. The key contribution is an algorithmic innovation that respects the physical nature of…

This work proposes an approach for latent-dynamics learning that exactly enforces physical conservation laws. The method comprises two steps. First, the method computes a low-dimensional embedding of the high-dimensional dynamical-system…

Understanding complex systems with their reduced model is one of the central roles in scientific activities. Although physics has greatly been developed with the physical insights of physicists, it is sometimes challenging to build a…

Neural network models have shown outstanding performance and successful resolutions to complex problems in various fields. However, the majority of these models are viewed as black-box, requiring a significant amount of data for…

For real-life nonlinear systems, the exact form of nonlinearity is often not known and the known governing equations are often based on certain assumptions and approximations. Such representation introduced model-form error into the system.…