Related papers: Accurately Solving Physical Systems with Graph Lea…
We consider the problem of learning a graph from a finite set of noisy graph signal observations, the goal of which is to find a smooth representation of the graph signal. Such a problem is motivated by the desire to infer relational…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
An expeditious development of graph learning in recent years has found innumerable applications in several diversified fields. Of the main associated challenges are the volume and complexity of graph data. The graph learning models suffer…
Physics-informed neural networks solve partial differential equations by training neural networks. Since this method approximates infinite-dimensional PDE solutions with finite collocation points, minimizing discretization errors by…
Combinatorial optimization problems near algorithmic phase transitions represent a fundamental challenge for both classical algorithms and machine learning approaches. Among them, graph coloring stands as a prototypical constraint…
The recent rise of deep learning has led to numerous applications, including solving partial differential equations using Physics-Informed Neural Networks. This approach has proven highly effective in several academic cases. However, their…
The position-based dynamics (PBD) algorithm is a popular and versatile technique for real-time simulation of deformable bodies, but is only applicable to forces that can be expressed as linearly compliant constraints. In this work, we…
Data-driven approaches have been proven effective in solving combinatorial optimization problems over graphs such as the traveling salesman problems and the vehicle routing problem. The rationale behind such methods is that the input…
Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…
Recent progress in research on Deep Graph Networks (DGNs) has led to a maturation of the domain of learning on graphs. Despite the growth of this research field, there are still important challenges that are yet unsolved. Specifically,…
Goal-conditioned rearrangement of deformable objects (e.g. straightening a rope and folding a cloth) is one of the most common deformable manipulation tasks, where the robot needs to rearrange a deformable object into a prescribed goal…
Recent advances show that neural networks embedded with physics-informed priors significantly outperform vanilla neural networks in learning and predicting the long term dynamics of complex physical systems from noisy data. Despite this…
Predictive models are a crucial component of many robotic systems. Yet, constructing accurate predictive models for a variety of deformable objects, especially those with unknown physical properties, remains a significant challenge. This…
Molecular dynamics (MD) simulations enable the study of the motion of small and large (bio)molecules and the estimation of their conformational ensembles. The description of the environment (solvent) has thereby a large impact. Implicit…
Physics-based simulation of mesh based domains remains a challenging task. State-of-the-art techniques can produce realistic results but require expert knowledge. A major bottleneck in many approaches is the step of integrating a potential…
Recently, the application of machine learning models has gained momentum in natural sciences and engineering, which is a natural fit due to the abundance of data in these fields. However, the modeling of physical processes from simulation…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and…
In this paper we present a deep learning method to predict the temporal evolution of dissipative dynamic systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting…
The objective of pose SLAM or pose-graph optimization (PGO) is to estimate the trajectory of a robot given odometric and loop closing constraints. State-of-the-art iterative approaches typically involve the linearization of a non-convex…