Related papers: Embedding physical symmetries into machine-learned…
Data-driven machine learning models often require extensive datasets, which can be costly or inaccessible, and their predictions may fail to comply with established physical laws. Current approaches for incorporating physical priors…
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…
Data augmentation is a powerful mechanism in equivariant machine learning, encouraging symmetry by training networks to produce consistent outputs under transformed inputs. Yet, effective augmentation typically requires the underlying…
The many ways in which machine and deep learning are transforming the analysis and simulation of data in particle physics are reviewed. The main methods based on boosted decision trees and various types of neural networks are introduced,…
Large language models (LLMs) are pretrained by minimizing the cross-entropy loss for next-token prediction. In this paper, we study whether this optimization strategy can induce geometric structure in the learned model weights and context…
Classification algorithms have recently found applications in computational physics for the selection of numerical methods or models adapted to the environment and the state of the physical system. For such classification tasks, labeled…
Deep learning and data-driven approaches have shown great potential in scientific domains. The promise of data-driven techniques relies on the availability of a large volume of high-quality training datasets. Due to the high cost of…
Overparameterized models have proven to be powerful tools for solving various machine learning tasks. However, overparameterization often leads to a substantial increase in computational and memory costs, which in turn requires extensive…
The excellent performance of deep neural networks is usually accompanied by a large number of parameters and computations, which have limited their usage on the resource-limited edge devices. To address this issue, abundant methods such as…
Data augmentation is commonly used to encode invariances in learning methods. However, this process is often performed in an inefficient manner, as artificial examples are created by applying a number of transformations to all points in the…
This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…
Recognizing symmetries in data allows for significant boosts in neural network training, which is especially important where training data are limited. In many cases, however, the exact underlying symmetry is present only in an idealized…
Symmetry transformations induce invariances which are frequently described with deep latent variable models. In many complex domains, such as the chemical space, invariances can be observed, yet the corresponding symmetry transformation…
In a landscape where scientific discovery is increasingly driven by data, the integration of machine learning (ML) with traditional scientific methodologies has emerged as a transformative approach. This paper introduces a novel,…
Symmetries are fundamental to both turbulence and differential equations. The large-eddy simulation (LES) equations inherit these symmetries provided the LES closure respects them. Classical LES closures based on eddy viscosity or scale…
A data-driven model augmentation framework, referred to as Weakly-coupled Integrated Inference and Machine Learning (IIML), is presented to improve the predictive accuracy of physical models. In contrast to parameter calibration, this work…
Identifying model parameters from observed configurations poses a fundamental challenge in data science, especially with limited data. Recently, diffusion models have emerged as a novel paradigm in generative machine learning, capable of…
The unprecedented amount of data generated from experiments, field observations, and large-scale numerical simulations at a wide range of spatio-temporal scales have enabled the rapid advancement of data-driven and especially deep learning…
Exploiting symmetry in dynamical systems is a powerful way to improve the generalization of deep learning. The model learns to be invariant to transformation and hence is more robust to distribution shift. Data augmentation and equivariant…
Data augmentation is a key element in training high-dimensional models. In this approach, one synthesizes new observations by applying pre-specified transformations to the original training data; e.g.~new images are formed by rotating old…