相关论文: A PAC-Bayesian View of Generalisation for Physics-…

In a landscape where scientific discovery is increasingly driven by data, the integration of machine learning (ML) with traditional scientific methodologies has emerged as a transformative approach. This paper introduces a novel,…

Control policies from imitation learning can often fail to generalize to novel environments due to imperfect demonstrations or the inability of imitation learning algorithms to accurately infer the expert's policies. In this paper, we…

We present a novel class of Physics-Informed Neural Networks that is formulated based on the principles of Evidential Deep Learning, where the model incorporates uncertainty quantification by learning parameters of a higher-order…

Deep learning has shown strong potential in modeling complex spatiotemporal dynamics. However, most existing methods depend on densely and uniformly sampled data, which is often unavailable in practice due to sensor and cost limitations. In…

Despite recent advances in its theoretical understanding, there still remains a significant gap in the ability of existing PAC-Bayesian theories on meta-learning to explain performance improvements in the few-shot learning setting, where…

PAC-Bayesian bounds are known to be tight and informative when studying the generalization ability of randomized classifiers. However, they require a loose and costly derandomization step when applied to some families of deterministic…

Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…

Accurate representations of unknown and sub-grid physical processes through parameterizations (or closure) in numerical simulations with quantified uncertainty are critical for resolving the coarse-grained partial differential equations…

Meta learning automatically infers an inductive bias, that includes the hyperparameter of the base-learning algorithm, by observing data from a finite number of related tasks. This paper studies PAC-Bayes bounds on meta generalization gap.…

Modern machine learning usually involves predictors in the overparameterised setting (number of trained parameters greater than dataset size), and their training yields not only good performance on training data, but also good…

Regularizing continual learning techniques is important for anticipating algorithmic behavior under new realizations of data. We introduce a new approach to continual learning by imposing the properties of a parabolic partial differential…

Meta-learning can successfully acquire useful inductive biases from data. Yet, its generalization properties to unseen learning tasks are poorly understood. Particularly if the number of meta-training tasks is small, this raises concerns…

The physics-based modeling has been the workhorse for many decades in many scientific and engineering applications ranging from wind power, weather forecasting, and aircraft design. Recently, data-driven models are increasingly becoming…

By leveraging experience from previous tasks, meta-learning algorithms can achieve effective fast adaptation ability when encountering new tasks. However it is unclear how the generalization property applies to new tasks. Probably…

The ability of overparameterized deep networks to generalize well has been linked to the fact that stochastic gradient descent (SGD) finds solutions that lie in flat, wide minima in the training loss -- minima where the output of the…

We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…

Symmetries are known to improve the empirical performance of machine learning models, yet theoretical guarantees explaining these gains remain limited. Prior work has focused mainly on compact group symmetries and often assumes that the…

Supervised machine learning involves approximating an unknown functional relationship from a limited dataset of features and corresponding labels. The classical approach to feature-based machine learning typically relies on applying linear…

We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines spatial-spectral…

Off-policy learning (OPL) often involves minimizing a risk estimator based on importance weighting to correct bias from the logging policy used to collect data. However, this method can produce an estimator with a high variance. A common…