Related papers: PICL: Physics Informed Contrastive Learning for Pa…

A kernel-based approach for the learning of the solution operator of general nonhomogeneous partial differential equations (PDEs) is proposed. The method incorporates physical priors, typically encoded through the PDE operator, into a…

Physics-Informed Neural Networks (PINNs) can be regarded as general-purpose PDE solvers, but it might be slow to train PINNs on particular problems, and there is no theoretical guarantee of corresponding error bounds. In this manuscript, we…

Predicting outcomes and planning interactions with the physical world are long-standing goals for machine learning. A variety of such tasks involves continuous physical systems, which can be described by partial differential equations…

Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training…

Preserving maximal information is one of principles of designing self-supervised learning methodologies. To reach this goal, contrastive learning adopts an implicit way which is contrasting image pairs. However, we believe it is not fully…

Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…

Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting…

Physics-informed neural networks (PINNs) offer a promising avenue for tackling both forward and inverse problems in partial differential equations (PDEs) by incorporating deep learning with fundamental physics principles. Despite their…

Physics-Informed Neural Networks (PINNs), which incorporate PDEs as soft constraints, train with a composite loss function that contains multiple training point types: different types of collocation points chosen during training to enforce…

Physics-informed neural networks (PINNs) have made significant strides in modeling dynamical systems governed by partial differential equations (PDEs). However, their generalization capabilities across varying scenarios remain limited. To…

Partial differential equations (PDEs) govern nearly every physical process in science and engineering, yet solving them at scale remains prohibitively expensive. Generative AI has transformed language, vision, and protein science, but…

Physics-Informed Neural Networks (PINNs) combine deep learning with physical constraints for solving partial differential equations (PDEs), and are widely applied in fluid mechanics, heat transfer, and solid mechanics. However, PINN…

Self-supervised representation learning has achieved impressive empirical success, yet its theoretical understanding remains limited. In this work, we provide a theoretical perspective by formulating self-supervised representation learning…

Contrastive learning is a popular form of self-supervised learning that encourages augmentations (views) of the same input to have more similar representations compared to augmentations of different inputs. Recent attempts to theoretically…

Contrastive learning has made considerable progress in computer vision, outperforming supervised pretraining on a range of downstream datasets. However, is contrastive learning the better choice in all situations? We demonstrate two cases…

Unpaired image-to-image translation involves learning mappings between source domain and target domain in the absence of aligned or corresponding samples. Score based diffusion models have demonstrated state-of-the-art performance in…

Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…

Using responses generated by high-performing large language models (LLMs) for instruction tuning has become a widely adopted approach. However, the existing literature overlooks a property of LLM-generated responses: they conflate world…

Self-supervised contrastive learning frameworks have progressed rapidly over the last few years. In this paper, we propose a novel loss function for contrastive learning. We model our pre-training task as a binary classification problem to…

Contrastive pretraining can substantially increase model generalisation and downstream performance. However, the quality of the learned representations is highly dependent on the data augmentation strategy applied to generate positive…