Related papers: PICL: Physics Informed Contrastive Learning for Pa…
We generalize the theory of supervised contrastive learning, previously applied to physical systems at equilibrium or steady state, to systems following any dynamics described by coupled ordinary differential equations. We show that if…
Physics-informed neural networks solve partial differential equations by training neural networks. Since this method approximates infinite-dimensional PDE solutions with finite collocation points, minimizing discretization errors by…
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…
We propose a framework using contrastive learning as a pre-training task to perform image classification in the presence of noisy labels. Recent strategies such as pseudo-labeling, sample selection with Gaussian Mixture models, weighted…
Under partial-label learning (PLL) where, for each training instance, only a set of ambiguous candidate labels containing the unknown true label is accessible, contrastive learning has recently boosted the performance of PLL on vision…
A primary challenge of physics-informed machine learning (PIML) is its generalization beyond the training domain, especially when dealing with complex physical problems represented by partial differential equations (PDEs). This paper aims…
In this work we address supervised learning of neural networks via lifted network formulations. Lifted networks are interesting because they allow training on massively parallel hardware and assign energy models to discriminatively trained…
Neural surrogates for partial differential equations (PDEs) have become popular due to their potential to quickly simulate physics. With a few exceptions, neural surrogates generally treat the forward evolution of time-dependent PDEs as a…
Structured prediction involves learning to predict complex structures rather than simple scalar values. The main challenge arises from the non-Euclidean nature of the output space, which generally requires relaxing the problem formulation.…
Physics-informed neural operators (PINOs) have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). Recent research has demonstrated that incorporating Lie point symmetry information can…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
Partial differential equation (PDE)-constrained optimization arises in many scientific and engineering domains, such as energy systems, fluid dynamics and material design. In these problems, the decision variables (e.g., control inputs or…
Physics-informed neural networks (PINNs) have emerged as promising surrogate modes for solving partial differential equations (PDEs). Their effectiveness lies in the ability to capture solution-related features through neural networks.…
Partial differential equations (PDEs) govern a wide range of physical systems, but solving them efficiently remains a major challenge. The idea of a scientific foundation model (SciFM) is emerging as a promising tool for learning…
Physics-Informed Neural Networks (PINNs) often suffer from slow convergence, training instability, and reduced accuracy on challenging partial differential equations due to the anisotropic and rapidly varying geometry of their loss…
For years, adversarial training has been extensively studied in natural language processing (NLP) settings. The main goal is to make models robust so that similar inputs derive in semantically similar outcomes, which is not a trivial…
Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foundation model for scientific problems, named PROSE-PDE. Our…
Partial differential equations (PDEs) form the backbone of simulations of many natural phenomena, for example in climate modeling, material science, and even financial markets. The application of physics-informed neural networks to…
Solving partial differential equations (PDEs) can be prohibitively expensive using traditional numerical methods. Deep learning-based surrogate models typically specialize in a single PDE with fixed parameters. We present a framework for…
This letter presents a high-dimensional analysis of the training dynamics for a single-layer nonlinear contrastive learning model. The empirical distribution of the model weights converges to a deterministic measure governed by a…