Related papers: Discovering Physics Laws of Dynamical Systems via …

We develop a novel physics informed deep learning approach for solving nonlinear drift-diffusion equations on metric graphs. These models represent an important model class with a large number of applications in areas ranging from transport…

The puzzle of computer vision might find new challenging solutions when we realize that most successful methods are working at image level, which is remarkably more difficult than processing directly visual streams, just as happens in…

Complex systems manifest a small number of instabilities and bifurcations that are canonical in nature, resulting in universal pattern forming characteristics as a function of some parametric dependence. Such parametric instabilities are…

Dynamical systems are found in innumerable forms across the physical and biological sciences, yet all these systems fall naturally into universal equivalence classes: conservative or dissipative, stable or unstable, compressible or…

We propose a systematic method for learning stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle. The learned dynamics are autonomous ordinary…

Inverse problems involving differential equations often require identifying unknown parameters or functions from data. Existing approaches, such as Physics-Informed Neural Networks (PINNs), Universal Differential Equations (UDEs) and…

We propose a novel composite framework to find unknown fields in the context of inverse problems for partial differential equations (PDEs). We blend the high expressibility of deep neural networks as universal function estimators with the…

Progress towards the energy breakthroughs needed to combat climate change can be significantly accelerated through the efficient simulation of atomic systems. Simulation techniques based on first principles, such as Density Functional…

As traditional machine learning tools are increasingly applied to science and engineering applications, physics-informed methods have emerged as effective tools for endowing inferences with properties essential for physical realizability.…

Efficient exploration remains a challenging problem in reinforcement learning, especially for tasks where extrinsic rewards from environments are sparse or even totally disregarded. Significant advances based on intrinsic motivation show…

Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…

Rapid autonomous traversal of unstructured terrain is essential for scenarios such as disaster response, search and rescue, or planetary exploration. As a vehicle navigates at the limit of its capabilities over extreme terrain, its dynamics…

Neural Ordinary Differential Equations (NODEs) often struggle to adapt to new dynamic behaviors caused by parameter changes in the underlying physical system, even when these dynamics are similar to previously observed behaviors. This…

Continuous state spaces and stochastic, switching dynamics characterize a number of rich, realworld domains, such as robot navigation across varying terrain. We describe a reinforcementlearning algorithm for learning in these domains and…

This study presents the application of variable-order (VO) fractional calculus to the modeling of nonlocal solids. The reformulation of nonlocal fractional-order continuum mechanic framework, by means of VO kinematics, enables a unique…

We introduce a notion of emergence for coarse-grained macroscopic variables associated with highly-multivariate microscopic dynamical processes, in the context of a coupled dynamical environment. Dynamical independence instantiates the…

We investigate neural ordinary and stochastic differential equations (neural ODEs and SDEs) to model stochastic dynamics in fully and partially observed environments within a model-based reinforcement learning (RL) framework. Through a…

Distilling interpretable physical laws from videos has led to expanded interest in the computer vision community recently thanks to the advances in deep learning, but still remains a great challenge. This paper introduces an end-to-end…

Learning physical dynamics from data is a fundamental challenge in machine learning and scientific modeling. Real-world observational data are inherently incomplete and irregularly sampled, posing significant challenges for existing…

Conservation laws are key theoretical and practical tools for understanding, characterizing, and modeling nonlinear dynamical systems. However, for many complex systems, the corresponding conserved quantities are difficult to identify,…