相关论文: Lagrangian Neural Networks

Logic-based problems such as planning, theorem proving, or puzzles, typically involve combinatoric search and structured knowledge representation. Artificial neural networks are very successful statistical learners, however, for many years,…

We introduce neural Markov logic networks (NMLNs), a statistical relational learning system that borrows ideas from Markov logic. Like Markov logic networks (MLNs), NMLNs are an exponential-family model for modelling distributions over…

Feed-forward, fully-connected Artificial Neural Networks (ANNs) or the so-called Multi-Layer Perceptrons (MLPs) are well-known universal approximators. However, their learning performance varies significantly depending on the function or…

Graph neural networks (GNNs) are powerful machine learning models for various graph learning tasks. Recently, the limitations of the expressive power of various GNN models have been revealed. For example, GNNs cannot distinguish some…

Physical phenomena in the real world are often described by energy-based modeling theories, such as Hamiltonian mechanics or the Landau theory, which yield various physical laws. Recent developments in neural networks have enabled the…

In this paper we study a constraint-based representation of neural network architectures. We cast the learning problem in the Lagrangian framework and we investigate a simple optimization procedure that is well suited to fulfil the…

The goal of generative models is to learn the intricate relations between the data to create new simulated data, but current approaches fail in very high dimensions. When the true data generating process is based on physical processes these…

Mesh-free numerical methods offer flexibility in discretising complex geometries, showing potential where mesh-based methods struggle. While high-order approximations can be obtained via consistency correction using linear systems, they…

This paper addresses the need for deep learning models to integrate well-defined constraints into their outputs, driven by their application in surrogate models, learning with limited data and partial information, and scenarios requiring…

The solution of problems in physics is often facilitated by a change of variables. In this work we present neural transformations to learn symmetries of Hamiltonian mechanical systems. Maintaining the Hamiltonian structure requires novel…

Laplacian regularized stratified models (LRSM) are models that utilize the explicit or implicit network structure of the sub-problems as defined by the categorical features called strata (e.g., age, region, time, forecast horizon, etc.),…

Data-driven modeling of physical systems often relies on learning both positions and momenta to accurately capture Hamiltonian dynamics. However, in many practical scenarios, only position measurements are readily available. In this work,…

Neural networks can be used to identify phases and phase transitions in condensed matter systems via supervised machine learning. Readily programmable through modern software libraries, we show that a standard feed-forward neural network…

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…

This paper examines the coincidence of neural networks with numerical methods for solving spatiotemporal physical problems. Neural networks are used to learn predictive numerical models from trajectory datasets from two well understood 1D…

The H\"uckel Hamiltonian is an incredibly simple tight-binding model famed for its ability to capture qualitative physics phenomena arising from electron interactions in molecules and materials. Part of its simplicity arises from using only…

Long-range sequence modeling is a crucial aspect of natural language processing and time series analysis. However, traditional models like Recurrent Neural Networks (RNNs) and Transformers suffer from computational and memory…

We propose a learning paradigm for numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework is…

We introduce a new method, called CNNAS (convolutional neural networks for atomistic systems), for calculating the total energy of atomic systems which rivals the computational cost of empirical potentials while maintaining the accuracy of…

We propose a method for efficiently incorporating constraints into a stochastic gradient Langevin framework for the training of deep neural networks. Constraints allow direct control of the parameter space of the model. Appropriately…