Related papers: Denoising Hamiltonian Network for Physical Reasoni…

Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's…

This work introduces a new framework integrating port-Hamiltonian systems (PHS) and neural network architectures. This framework bridges the gap between deterministic and stochastic modeling of complex dynamical systems. We introduce new…

Designing neural networks within a Hamiltonian framework offers a principled way to ensure that conservation laws are respected in physical systems. While promising, these capabilities have been largely limited to discrete, analytically…

In this paper, we introduce a physics-driven regularization method for training of deep neural networks (DNNs) for use in engineering design and analysis problems. In particular, we focus on prediction of a physical system, for which in…

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 Deep Material Network (DMN) has emerged as a powerful framework for multiscale materials modeling, enabling efficient and accurate prediction of material behavior across different length scales. Unlike conventional data-driven…

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…

As a network-based functional approximator, we have proposed a "Lagrangian Density Space-Time Deep Neural Networks" (LDDNN) topology. It is qualified for unsupervised training and learning to predict the dynamics of underlying physical…

Hamiltonian learning (HL), enabling precise estimation of system parameters and underlying dynamics, plays a critical role in characterizing quantum systems. However, conventional HL methods face challenges in noise robustness and resource…

The fundamental laws of physics are intrinsically geometric, dictating the evolution of systems through principles of symmetry and conservation. While modern machine learning offers powerful tools for modeling complex dynamics from data,…

Conventional neural networks are universal function approximators, but because they are unaware of underlying symmetries or physical laws, they may need impractically many training data to approximate nonlinear dynamics. Recently introduced…

Despite prior advances in PINNs, significant challenges remain in localized solid mechanics problems because of the limitations of single network formulations in simultaneous resolution of smooth global responses and near-tip singularities,…

We propose a novel framework based on neural network that reformulates classical mechanics as an operator learning problem. A machine directly maps a potential function to its corresponding trajectory in phase space without solving the…

Hybrid machine learning based on Hamiltonian formulations has recently been successfully demonstrated for simple mechanical systems, both energy conserving and not energy conserving. We introduce a pseudo-Hamiltonian formulation that is a…

Physics-informed deep learning models have emerged as powerful tools for learning dynamical systems. These models directly encode physical principles into network architectures. However, systematic benchmarking of these approaches across…

Deep hedging represents a cutting-edge approach to risk management for financial derivatives by leveraging the power of deep learning. However, existing methods often face challenges related to computational inefficiency, sensitivity to…

Lagrangian Neural Networks (LNNs) are a powerful tool for addressing physical systems, particularly those governed by conservation laws. LNNs can parametrize the Lagrangian of a system to predict trajectories with nearly conserved energy.…

Image decomposition aims to analyze an image into elementary components, which is essential for numerous downstream tasks and also by nature provides certain interpretability to the analysis. Deep learning can be powerful for such tasks,…

Deep learning has achieved astonishing results on many tasks with large amounts of data and generalization within the proximity of training data. For many important real-world applications, these requirements are unfeasible and additional…

Deep learning has been widely used within learning algorithms for robotics. One disadvantage of deep networks is that these networks are black-box representations. Therefore, the learned approximations ignore the existing knowledge of…