Related papers: Unsupervised operator learning approach for dissip…

Derivative-Informed Operator Learning (DIOL), i.e. learning a (nonlinear) operator and its derivatives, is an open research frontier at the foundations of the influential field of Operator Learning (OL). In particular, Universal…

We propose a novel fine-tuning method to achieve multi-operator learning through training a distributed neural operator with diverse function data and then zero-shot fine-tuning the neural network using physics-informed losses for…

Data-driven learning of partial differential equations' solution operators has recently emerged as a promising paradigm for approximating the underlying solutions. The solution operators are usually parameterized by deep learning models…

The stochastic and dynamic nature of renewable energy sources and power electronic devices are creating unique challenges for modern power systems. One such challenge is that the conventional mathematical systems models-based optimal active…

Deep Neural Networks (DNNs) are typically trained by backpropagation in a batch learning setting, which requires the entire training data to be made available prior to the learning task. This is not scalable for many real-world scenarios…

Learning dynamical systems through operator-theoretic representations provides a powerful framework for analyzing complex dynamics, as spectral quantities such as eigenvalues and invariant structures encode characteristic time scales and…

Reaction-diffusion (RD) equations underpin pattern formation across chemistry, biology, and physics, yet learning stable operators that forecast their long-term dynamics from data remains challenging. Neural-operator surrogates provide…

We propose a thermodynamics-based learning strategy for non-equilibrium evolution equations based on Onsager's variational principle, which allows to write such PDEs in terms of two potentials: the free energy and the dissipation potential.…

Deep neural networks (DNNs) recently emerged as a promising tool for analyzing and solving complex differential equations arising in science and engineering applications. Alternative to traditional numerical schemes, learning-based solvers…

Recent years have witnessed the promise of coupling machine learning methods and physical domain-specific insights for solving scientific problems based on partial differential equations (PDEs). However, being data-intensive, these methods…

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…

Operator learning focuses on approximating mappings $\mathcal{G}^\dagger:\mathcal{U} \rightarrow\mathcal{V}$ between infinite-dimensional spaces of functions, such as $u: \Omega_u\rightarrow\mathbb{R}$ and $v:…

Neural ordinary differential equations (NODEs), one of the most influential works of the differential equation-based deep learning, are to continuously generalize residual networks and opened a new field. They are currently utilized for…

We present DDFlow, a data distillation approach to learning optical flow estimation from unlabeled data. The approach distills reliable predictions from a teacher network, and uses these predictions as annotations to guide a student network…

Modern over-parameterized deep models are highly data-dependent, with large scale general-purpose and domain-specific datasets serving as the bedrock for rapid advancements. However, many datasets are proprietary or contain sensitive…

Offline imitation learning (IL) is a powerful method to solve decision-making problems from expert demonstrations without reward labels. Existing offline IL methods suffer from severe performance degeneration under limited expert data.…

Domain adaptation (DA) aims to enable a learning model trained from a source domain to generalize well on a target domain, despite the mismatch of data distributions between the two domains. State-of-the-art DA methods have so far focused…

Unsupervised learning has been extensively adopted to train deep neural networks (DNNs) for learning wireless resource allocation. Yet, the performance of DNNs is vulnerable to distribution shifts between training and test data, e.g.,…

Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…

Large-scale deep learning models contribute to significant performance improvements on varieties of downstream tasks. Current data and model parallelism approaches utilize model replication and partition techniques to support the…