相关论文: Neural non-canonical Hamiltonian dynamics for long…
Quantum dynamics simulations (QDSs) are one of the most highly anticipated applications of quantum computing. Quantum circuit depth for implementing Hamiltonian simulation algorithms is commonly time dependent so that long time dynamics…
The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations.…
Model-based Reinforcement Learning and Control have demonstrated great potential in various sequential decision making problem domains, including in robotics settings. However, real-world robotics systems often present challenges that limit…
Machine learning has become increasingly popular for efficiently modelling the dynamics of complex physical systems, demonstrating a capability to learn effective models for dynamics which ignore redundant degrees of freedom. Learned…
We study the problem of Hamiltonian structure learning from real-time evolution: given the ability to apply $e^{-\mathrm{i} Ht}$ for an unknown local Hamiltonian $H = \sum_{a = 1}^m \lambda_a E_a$ on $n$ qubits, the goal is to recover $H$.…
Numerical modeling of different structural materials that have highly nonlinear behaviors has always been a challenging problem in engineering disciplines. Experimental data is commonly used to characterize this behavior. This study aims to…
Evolution has resulted in highly developed abilities in many natural intelligences to quickly and accurately predict mechanical phenomena. Humans have successfully developed laws of physics to abstract and model such mechanical phenomena.…
Chaotic systems, such as turbulent flows, are ubiquitous in science and engineering. However, their study remains a challenge due to the large range scales, and the strong interaction with other, often not fully understood, physics. As a…
Recent advances in deep learning for physics have focused on discovering shared representations of target systems by incorporating physics priors or inductive biases into neural networks. While effective, these methods are limited to the…
Machine learning methods are widely used in the natural sciences to model and predict physical systems from observation data. Yet, they are often used as poorly understood "black boxes," disregarding existing mathematical structure and…
The equations of classical mechanics can be used to model the time evolution of countless physical systems, from the astrophysical to the atomic scale. Accurate numerical integration requires small time steps, which limits the computational…
Learning continuous-time dynamics on complex networks is crucial for understanding, predicting and controlling complex systems in science and engineering. However, this task is very challenging due to the combinatorial complexities in the…
Robotic manipulation can greatly benefit from the data efficiency, robustness, and predictability of model-based methods if robots can quickly generate models of novel objects they encounter. This is especially difficult when effects like…
Symplectic schemes are powerful methods for numerically integrating Hamiltonian systems, and their long-term accuracy and fidelity have been proved both theoretically and numerically. However direct applications of standard symplectic…
This paper proposes Hamiltonian Learning, a novel unified framework for learning with neural networks "over time", i.e., from a possibly infinite stream of data, in an online manner, without having access to future information. Existing…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In…
Learning to simulate complex physical systems from data has emerged as a promising way to overcome the limitations of traditional numerical solvers, which often require prohibitive computational costs for high-fidelity solutions. Recent…
Learning models for dynamical systems in continuous time is significant for understanding complex phenomena and making accurate predictions. This study presents a novel approach utilizing differential neural networks (DNNs) to model…
Numerical simulators are essential tools in the study of natural fluid-systems, but their performance often limits application in practice. Recent machine-learning approaches have demonstrated their ability to accelerate spatio-temporal…