Related papers: Energy Loss Functions for Physical Systems
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…
The solution of complex many-body lattice models can often be found by defining an energy functional of the relevant density of the problem. For instance, in the case of the Hubbard model the spin-resolved site occupation is enough to…
The inverse Ising problem and its generalizations to Potts and continuous spin models have recently attracted much attention thanks to their successful applications in the statistical modeling of biological data. In the standard setting,…
With economic development, the complexity of infrastructure has increased drastically. Similarly, with the shift from fossil fuels to renewable sources of energy, there is a dire need for such systems that not only predict and forecast with…
We develop a framework for dualizing the Kolmogorov structure function $h_x(\alpha)$, which then allows using computable complexity proxies. We establish a mathematical analogy between information-theoretic constructs and statistical…
Voltage prediction in distribution grids is a critical yet difficult task for maintaining power system stability. Machine learning approaches, particularly Graph Neural Networks (GNNs), offer significant speedups but suffer from poor…
Physics Informed Neural Networks (PINNs) is a promising application of deep learning. The smooth architecture of a fully connected neural network is appropriate for finding the solutions of PDEs; the corresponding loss function can also be…
We offer an insight into our mathematical endeavors, which aim to advance the foundational understanding of energy systems in a broad context, encompassing facets such as charge transport, energy storage, markets, and collective behavior.…
Model-based geostatistical design involves the selection of locations to collect data to minimise an expected loss function over a set of all possible locations. The loss function is specified to reflect the aim of data collection, which,…
Machine learning (ML) is transforming all areas of science. The complex and time-consuming calculations in molecular simulations are particularly suitable for a machine learning revolution and have already been profoundly impacted by the…
Typically, loss functions, regularization mechanisms and other important aspects of training parametric models are chosen heuristically from a limited set of options. In this paper, we take the first step towards automating this process,…
Machine learning models have emerged as a very effective strategy to sidestep time-consuming electronic-structure calculations, enabling accurate simulations of greater size, time scale and complexity. Given the interpolative nature of…
We propose Energy-based generator matching (EGM), a modality-agnostic approach to train generative models from energy functions in the absence of data. Extending the recently proposed generator matching, EGM enables training of arbitrary…
Machine-learning potentials are usually trained on the ground-state, Born-Oppenheimer energy surface, which depends exclusively on the atomic positions and not on the simulation temperature. This disregards the effect of thermally-excited…
We train an equivariant machine learning model to predict energies and forces for a real-world study of hydrogen combustion under conditions of finite temperature and pressure. This challenging case for reactive chemistry illustrates that…
Being able to quickly adapt to changes in dynamics is paramount in model-based control for object manipulation tasks. In order to influence fast adaptation of the inverse dynamics model's parameters, data efficiency is crucial. Given…
Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…
Accurate prediction of energy and forces for 3D molecular systems is one of fundamental challenges at the core of AI for Science applications. Many powerful and data-efficient neural networks predict molecular energies and forces from…
The use of machine learning algorithms to predict behaviors of complex systems is booming. However, the key to an effective use of machine learning tools in multi-physics problems, including combustion, is to couple them to physical and…
Molecular dynamics (MD) simulations provide atomistic insight into biomolecular systems but are often limited by high computational costs required to access long timescales. Coarse-grained machine learning models offer a promising avenue…