A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New method learns from non-uniform data and partial physical knowledge.
Enhances neural operators with physics knowledge for more accurate simulations.
Framework augments physical models with deep learning for complex dynamics forecasting.
Framework uses physics knowledge to improve spatiotemporal prediction with limited data.
Novel framework for learning infinitesimal generator of stochastic processes.
Data-driven models analyze power grids under incomplete physical information, and their accuracy has been mostly validated empirically using certain training and testing datasets. This paper explores error bounds for data-driven models under all possible training and testing scenarios, and proposes an evaluation implem…
MUSIC learns coupled systems with sparse data and incomplete physics.
Centuries of development in natural sciences and mathematical modeling provide valuable domain expert knowledge that has yet to be explored for the development of machine learning models. When modeling complex physical systems, both domain knowledge and data provide necessary information about the system. In this paper…
AutoKE automates embedding physical knowledge into neural networks for complex engineering problems.
In this work, we propose a new Gaussian process regression (GPR)-based multifidelity method: physics-informed CoKriging (CoPhIK). In CoKriging-based multifidelity methods, the quantities of interest are modeled as linear combinations of multiple parameterized stationary Gaussian processes (GPs), and the hyperparameters…
The physics informed neural network (PINN) is evolving as a viable method to solve partial differential equations. In the recent past PINNs have been successfully tested and validated to find solutions to both linear and non-linear partial differential equations (PDEs). However, the literature lacks detailed investigat…
pVAE combines physics and machine learning for robust data representations.
Survey of integrating physics knowledge into machine learning models.
Meta-learning neural networks to solve diverse PDEs efficiently.
TIME network simplifies complex physical processes with interpretable models.
The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery (), decides which physical terms are necessary and which can be removed (because they are physically n…
An innovative physics-guided learning algorithm for predicting the mechanical response of materials and structures is proposed in this paper. The key concept of the proposed study is based on the fact that physics models are governed by Partial Differential Equation (PDE), and its loading/ response mapping can be solve…
Hybrid model combines physics and data to handle incomplete systems.
Adaptive learning of SPDE solutions using score-based diffusion models.
Machine learning improves planetary space physics by incorporating physical knowledge.
PIML uses physics equations in machine learning for better forecasting.
We infer both microscopic and macroscopic behaviors of a three-dimensional chaotic fluid flow using reservoir computing. In our procedure of the inference, we assume no prior knowledge of a physical process of a fluid flow except that its behavior is complex but deterministic. We present two ways of inference of the co…
While physics conveys knowledge of nature built from an interplay between observations and theory, it has been considered less importantly in deep neural networks. Especially, there are few works leveraging physics behaviors when the knowledge is given less explicitly. In this work, we propose a novel architecture call…
Proposes a physics-informed VAE for disentangling physics from confounding influences.
In this paper, we introduce a novel framework for combining scientific knowledge within physics-based models and recurrent neural networks to advance scientific discovery in many dynamical systems. We will first describe the use of outputs from physics-based models in learning a hybrid-physics-data model. Then, we furt…
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this two part treatise, we present our developments in the context of solving two main classes …
Paper develops error rates for physics-informed learning, comparing it to data-driven methods.
Paper integrates ML with physics models for engineering and environmental challenges.
PID-GAN uses physics knowledge to improve deep learning models' reliability.
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this second part of our two-part treatise, we focus on the problem of data-driven discovery of …
The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowledge. Such constraints are often imposed as soft penalties during model training and effectively act as domain-specific regularizers of the em…
EPGP priors solve linear PDEs from data.
Improved method using filtered PDEs for robust physics-informed deep learning.
Develops PAC-Bayesian framework for physics-informed machine learning.
We present a new hybrid physics-based machine-learning approach to reservoir modeling. The methodology relies on a series of deep adversarial neural network architecture with physics-based regularization. The network is used to simulate the dynamic behavior of physical quantities (i.e. saturation) subject to a set of g…
Physics-informed kernel learning integrates physical priors into machine learning models.
Bayesian model learns physics laws from data with uncertainty quantification.
Improves model accuracy for neural nets in stochastic dynamics with partial prior knowledge.
Bayesian PINNs learn elliptic PDEs with near-minimax posterior contraction rate.
Physics-constrained deep learning predicts geophysical dynamics with boundedness.
Arriving at the complete probabilistic knowledge of a domain, i.e., learning how all variables interact, is indeed a demanding task. In reality, settings often arise for which an individual merely possesses partial knowledge of the domain, and yet, is expected to give adequate answers to a variety of posed queries. Tha…
Unified physics-informed learning method improves generalization performance.
New method uses dynamic sampling to improve PINNs efficiency.
This paper introduces a framework for combining scientific knowledge of physics-based models with neural networks to advance scientific discovery. This framework, termed physics-guided neural networks (PGNN), leverages the output of physics-based model simulations along with observational features in a hybrid modeling …
There has been rapid progress recently on the application of deep networks to the solution of partial differential equations, collectively labelled as Physics Informed Neural Networks (PINNs). In this paper, we develop Physics Informed Extreme Learning Machine (PIELM), a rapid version of PINNs which can be applied to s…
In typical machine learning tasks and applications, it is necessary to obtain or create large labeled datasets in order to to achieve high performance. Unfortunately, large labeled datasets are not always available and can be expensive to source, creating a bottleneck towards more widely applicable machine learning. Th…
BITS for GAPS uses Bayesian methods to improve surrogate model accuracy in complex 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 particular, we introduce \emph{hidden physics models}, which are essentially data-efficien…