Related papers: Learning nonlocal constitutive models with neural …

We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…

This work presents a novel methodology for analysis and control of nonlinear fluid systems using neural networks. The approach is demonstrated on four different study cases being the Lorenz system, a modified version of the…

In this paper, we present a new data-driven method for learning stable models of nonlinear systems. Our model lifts the original state space to a higher-dimensional linear manifold using Koopman embeddings. Interestingly, we prove that…

Learning a task induces connectivity changes in neural circuits, thereby changing their dynamics. To elucidate task related neural dynamics we study trained Recurrent Neural Networks. We develop a Mean Field Theory for Reservoir Computing…

Soft biological tissues exhibit a tendency to maintain a preferred state of tensile stress, known as tensional homeostasis, which is restored even after external mechanical stimuli. This macroscopic behavior can be described using the…

Forecasting the future traffic flow distribution in an area is an important issue for traffic management in an intelligent transportation system. The key challenge of traffic prediction is to capture spatial and temporal relations between…

Constitutive models that describe the mechanical behavior of soft tissues have advanced greatly over the past few decades. These expert models are generalizable and require the calibration of a number of parameters to fit experimental data.…

Non-Newtonian fluid flow might be driven by spatially nonlocal velocity, the dynamics of which can be described by promising fractional derivative models. This short communication proposes a space FrActional-order Constitutive Equation…

A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…

In recent years, deep learning has proven to be a viable methodology for surrogate modeling and uncertainty quantification for a vast number of physical systems. However, in their traditional form, such models can require a large amount of…

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…

Recent findings show that deep convolutional neural networks (DCNNs) do not generalize well under partial occlusion. Inspired by the success of compositional models at classifying partially occluded objects, we propose to integrate…

In this paper, we address the issue of modeling and estimating changes in the state of the spatio-temporal dynamical systems based on a sequence of observations like video frames. Traditional numerical simulation systems depend largely on…

Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…

In this contribution, we present a new Materials Knowledge System framework for microstructure-sensitive predictions of effective stress--strain responses in composite materials. The model is developed for composites with a wide range of…

Throughout developmental biology and ecology, transport can be driven by nonlocal interactions. Examples include cells that migrate based on contact with pseudopodia extended from other cells, and animals that move based on their vision of…

(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…

The elastic properties of materials derive from their electronic and atomic nature. However, simulating bulk materials fully at these scales is not feasible, so that typically homogenized continuum descriptions are used instead. A seamless…

We present a scalable framework for learning deterministic and probabilistic neural surrogates for high-resolution 3D physics simulations. We introduce a hybrid CNN-Transformer backbone architecture targeted for 3D physics simulations,…

We have measured the nonlinear rheological response of a model transient network over a large range of steady shear rates. The system is built up from an oil in water droplet microemulsion into which a telechelic polymer is incorporated.…