Related papers: Solving and learning advective multiscale Darcian …

In this paper, we present a residual-driven multiscale method for simulating Darcy flow in perforated domains, where complex geometries and highly heterogeneous permeability make direct simulations computationally expensive. To address…

The integration of algorithmic components into neural architectures has gained increased attention recently, as it allows training neural networks with new forms of supervision such as ordering constraints or silhouettes instead of using…

With the recent wave of digitalization, specifically in the context of safety-critical applications, there has been a growing need for computationally efficient, accurate, generalizable, and trustworthy models. Physics-based models have…

The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the…

We revisit the problem of physics-informed regression, and propose a method that directly computes the state at the prediction point, simultaneously with the derivative and curvature information of the existing samples. We frame each…

Differential equations are used to model and predict the behaviour of complex systems in a wide range of fields, and the ability to solve them is an important asset for understanding and predicting the behaviour of these systems.…

Learning dynamics governing physical and spatiotemporal processes is a challenging problem, especially in scenarios where states are partially measured. In this work, we tackle the problem of learning dynamics governing these systems when…

Differentiable physics enables efficient gradient-based optimizations of neural network (NN) controllers. However, existing work typically only delivers NN controllers with limited capability and generalizability. We present a practical…

State-space estimation and tracking rely on accurate dynamical models to perform well. However, obtaining an vaccurate dynamical model for complex scenarios or adapting to changes in the system poses challenges to the estimation process.…

We introduce a methodology for seeking conservation laws within a Hamiltonian dynamical system, which we term ``neural deflation''. Inspired by deflation methods for steady states of dynamical systems, we propose to {iteratively} train a…

Assessing the systemic effects of uncertainty that arises from agents' partial observation of the true states of the world is critical for understanding a wide range of scenarios. Yet, previous modeling work on agent learning and…

We discuss nonlinear model predictive control (NMPC) for multi-body dynamics via physics-informed machine learning methods. Physics-informed neural networks (PINNs) are a promising tool to approximate (partial) differential equations. PINNs…

Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by…

We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this two part…

Control of non-episodic, finite-horizon dynamical systems with uncertain dynamics poses a tough and elementary case of the exploration-exploitation trade-off. Bayesian reinforcement learning, reasoning about the effect of actions and future…

Numerical simulation is indispensable in industrial design processes. It can replace expensive experiments and even reduce the need for prototypes. While products designed with the aid of numerical simulation undergo continuous improvement,…

Learning low-dimensional latent state space dynamics models has been a powerful paradigm for enabling vision-based planning and learning for control. We introduce a latent dynamics learning framework that is uniquely designed to induce…

Reinforcement learning is an appropriate and successful method to robustly perform low-level robot control under noisy conditions. Symbolic action planning is useful to resolve causal dependencies and to break a causally complex problem…

We explore how neural differential equations (NDEs) may be trained on highly resolved fluid-dynamical models of unresolved scales providing an ideal framework for data-driven parameterizations in climate models. NDEs overcome some of the…

The incorporation of appropriate inductive bias plays a critical role in learning dynamics from data. A growing body of work has been exploring ways to enforce energy conservation in the learned dynamics by encoding Lagrangian or…