Conventional reduced order modeling techniques such as the reduced basis (RB) method
(relying, eg, on proper orthogonal decomposition (POD)) may incur in severe limitations …

A data-driven framework is proposed towards the end of predictive modeling of complex
spatio-temporal dynamics, leveraging nested non-linear manifolds. Three levels of neural …

Nonlinear differential equations rarely admit closed-form solutions, thus requiring numerical
time-stepping algorithms to approximate solutions. Further, many systems characterized by …

Data-driven modeling continues to be enabled by modern machine learning algorithms and
deep learning architectures. The goals of such efforts revolve around the generation of …

This work proposes an extension of neural ordinary differential equations (NODEs) by
introducing an additional set of ODE input parameters to NODEs. This extension allows …

Real-time dynamic simulation remains a significant challenge for spatiotemporal data of
high dimension and resolution. In this study, we establish a transformer neural network …

Sensing is a universal task in science and engineering. Downstream tasks from sensing
include inferring full state estimates of a system (system identification), control decisions …

Projection-based reduced-order models (pROMs) show great promise as a means to
accelerate many-query applications such as forward error propagation, solving inverse …

We design a physics-aware auto-encoder to specifically reduce the dimensionality of
solutions arising from convection-dominated nonlinear physical systems. Although existing …

This work proposes a model-reduction approach for the material point method on nonlinear
manifolds. Our technique approximates the kinematics by approximating the deformation …