We introduce generative models for accelerating simulations of high-dimensional systems
through learning and evolving their effective dynamics. In the proposed Generative Learning …

We use physics-informed neural networks (PINNs) to numerically solve the discrete-time
nonlinear observer-based state estimation problem. Integrated within a single-step exact …

While many phenomena in physics and engineering are formally high-dimensional, their
long-time dynamics often live on a lower-dimensional manifold. The present work introduces …

In this work, we present the novel mathematical framework of latent dynamics models
(LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our …

Accurately modeling the electrochemical process of large-scale lithium-ion batteries (LLBs),
which involves estimating the electrochemical state distributions within the process, is …

Multiscale is a hallmark feature of complex systems, presenting challenges for traditional
numerical methods due to their reliance on local Taylor series constraints. Further …

Complex systems often show macroscopic coherent behavior due to the interactions of
microscopic agents like molecules, cells, or individuals in a population with their …

We introduce generative models for accelerating simulations of complex systems through
learning and evolving their effective dynamics. In the proposed Generative Learning of …

Partial Differential Equations are foundational in modeling science and natural systems such
as fluid dynamics and weather forecasting. The Latent Evolution of PDEs method is …

Establishing appropriate mathematical models for complex systems in natural phenomena
not only helps deepen our understanding of nature but can also be used for state estimation …