Related papers: Sobolev Training for Operator Learning

Many real-world systems are modelled using complex ordinary differential equations (ODEs). However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like Proper Orthogonal…

Operator learning, the approximation of mappings between infinite-dimensional function spaces using machine learning, has gained increasing research attention in recent years. Approximate operators, learned from data, can serve as efficient…

In this work, we propose ModelPred, a framework that helps to understand the impact of changes in training data on a trained model. This is critical for building trust in various stages of a machine learning pipeline: from cleaning…

We propose a method for training ordinary differential equations by using a control-theoretic Lyapunov condition for stability. Our approach, called LyaNet, is based on a novel Lyapunov loss formulation that encourages the inference…

This work presents a novel framework for physically consistent model error characterization and operator learning for reduced-order models of non-equilibrium chemical kinetics. By leveraging the Bayesian framework, we identify and infer…

The use of machine learning techniques to improve the performance of branch-and-bound optimization algorithms is a very active area in the context of mixed integer linear problems, but little has been done for non-linear optimization. To…

In this paper, we consider the use of prior knowledge within neural networks. In particular, we investigate the effect of a known transform within the mapping from input data space to the output domain. We demonstrate that use of known…

Quantum Machine Learning (QML) aims to leverage the principles of quantum mechanics to speed up the process of solving machine learning problems or improve the quality of solutions. Among these principles, entanglement with an auxiliary…

During the last few years, significant attention has been paid to the stochastic training of artificial neural networks, which is known as an effective regularization approach that helps improve the generalization capability of trained…

This work investigates the unexplored usability of self-supervised representation learning in the direction of functional knowledge transfer. In this work, functional knowledge transfer is achieved by joint optimization of self-supervised…

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…

We propose a structured prediction approach for robot imitation learning from demonstrations. Among various tools for robot imitation learning, supervised learning has been observed to have a prominent role. Structured prediction is a form…

In numerous contexts, high-resolution solutions to partial differential equations are required to capture faithfully essential dynamics which occur at small spatiotemporal scales, but these solutions can be very difficult and slow to obtain…

Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear…

Existing multimodal tasks mostly target at the complete input modality setting, i.e., each modality is either complete or completely missing in both training and test sets. However, the randomly missing situations have still been…

Most deep learning research has focused on developing new model and training procedures. On the other hand the training objective has usually been restricted to combinations of standard losses. When the objective aligns well with the…

While larger neural models are pushing the boundaries of what deep learning can do, often more weights are needed to train models rather than to run inference for tasks. This paper seeks to understand this behavior using search spaces --…

Reliable uncertainty quantification in deep neural networks is very crucial in safety-critical applications such as automated driving for trustworthy and informed decision-making. Assessing the quality of uncertainty estimates is…

Recent years have witnessed an abundance of new publications and approaches on meta-learning. This community-wide enthusiasm has sparked great insights but has also created a plethora of seemingly different frameworks, which can be hard to…

In recent years, self-supervised learning has played a pivotal role in advancing machine learning by allowing models to acquire meaningful representations from unlabeled data. An intriguing research avenue involves developing…