Related papers: Hamiltonian Neural Networks
Neural networks have emerged as a powerful way to approach many practical problems in quantum physics. In this work, we illustrate the power of deep learning to predict the dynamics of a quantum many-body system, where the training is…
The Hamiltonian formalism plays a central role in classical and quantum physics. Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful…
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…
Neural networks with binary weights are computation-efficient and hardware-friendly, but their training is challenging because it involves a discrete optimization problem. Surprisingly, ignoring the discrete nature of the problem and using…
This work focuses on learning non-canonical Hamiltonian dynamics from data, where long-term predictions require the preservation of structure both in the learned model and in numerical schemes. Previous research focused on either facet,…
We train a small message-passing graph neural network to predict Hamiltonian cycles on Erd\H{o}s-R\'enyi random graphs in a critical regime. It outperforms existing hand-crafted heuristics after about 2.5 hours of training on a single GPU.…
Neural networks leverage robust internal representations in order to generalise. Learning them is difficult, and often requires a large training set that covers the data distribution densely. We study a common setting where our task is not…
We propose a novel approach for learning the evolution that employs differentiable neural networks to approximate the full GENERIC structure. Instead of manually choosing the fitted parameters, we learn the whole model together with the…
In this Letter we supervisedly train neural networks to distinguish different topological phases in the context of topological band insulators. After training with Hamiltonians of one-dimensional insulators with chiral symmetry, the neural…
The success of the current wave of artificial intelligence can be partly attributed to deep neural networks, which have proven to be very effective in learning complex patterns from large datasets with minimal human intervention. However,…
The effectiveness of the Physics Informed Neural Networks (PINNs) for learning the dynamics of constrained Hamiltonian systems is demonstrated using the Dirac theory of constraints for regular systems with holonomic constraints and systems…
Recent advancements in quantum hardware and classical computing simulations have significantly enhanced the accessibility of quantum system data, leading to an increased demand for precise descriptions and predictions of these systems.…
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…
Data-driven algorithms, in particular neural networks, can emulate the effect of sub-grid scale processes in coarse-resolution climate models if trained on high-resolution climate simulations. However, they may violate key physical…
Learned world models excel at interpolative generalization but fail at extrapolative generalization to novel physical properties. This limitation arises because they learn statistical correlations rather than the environment's underlying…
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…
We explore unique considerations involved in fitting ML models to data with very high precision, as is often required for science applications. We empirically compare various function approximation methods and study how they scale with…
Concise, accurate descriptions of physical systems through their conserved quantities abound in the natural sciences. In data science, however, current research often focuses on regression problems, without routinely incorporating…
Understanding real-world dynamical phenomena remains a challenging task. Across various scientific disciplines, machine learning has advanced as the go-to technology to analyze nonlinear dynamical systems, identify patterns in big data, and…
Reconstructing a system Hamiltonian through measurements on its eigenstates is an important inverse problem in quantum physics. Recently, it was shown that generic many-body local Hamiltonians can be recovered by local measurements without…