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Physics-Informed Neural Networks (PINNs) are mesh-free approaches for the numerical approximation of partial differential equations, where a neural network is trained by minimizing a loss function derived from the governing equations and…

Randomized experiments are the preferred approach for evaluating the effects of interventions, but they are costly and often yield estimates with substantial uncertainty. On the other hand, in silico experiments leveraging foundation models…

When using reinforcement learning (RL) to tackle physical control tasks, inductive biases that encode physics priors can help improve sample efficiency during training and enhance generalization in testing. However, the current practice of…

In this paper, we further develop the approach, originating in [14 (arXiv:1311.6765),20 (arXiv:1604.02576)], to "computation-friendly" hypothesis testing and statistical estimation via Convex Programming. Specifically, we focus on…

Bayesian inverse problems use data to update a prior probability distribution on uncertain parameter values to a posterior distribution. Such problems arise in many structural engineering applications, but computational solution of Bayesian…

We consider class incremental learning (CIL) problem, in which a learning agent continuously learns new classes from incrementally arriving training data batches and aims to predict well on all the classes learned so far. The main challenge…

Diffusion models have emerged as powerful generative tools for modeling complex data distributions, yet their purely data-driven nature limits applicability in practical engineering and scientific problems where physical laws need to be…

In biomedical engineering, earthquake prediction, and underground energy harvesting, it is crucial to indirectly estimate the physical properties of porous media since the direct measurement of those are usually impractical/prohibitive.…

Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…

Safety is essential for reinforcement learning (RL) applied in the real world. Adding chance constraints (or probabilistic constraints) is a suitable way to enhance RL safety under uncertainty. Existing chance-constrained RL methods like…

Preference learning is critical for aligning large language models (LLMs) with human values, with the quality of preference datasets playing a crucial role in this process. While existing metrics primarily assess data quality based on…

Data-driven discovery of PDEs has made tremendous progress recently, and many canonical PDEs have been discovered successfully for proof-of-concept. However, determining the most proper PDE without prior references remains challenging in…

Informed learning is an emerging field in machine learning that aims to compensate for insufficient data with prior knowledge. Shape knowledge covers many types of prior knowledge concerning the relationship of a function's output with…

Penalized spline regression is a popular method for scatterplot smoothing, but there has long been a debate on how to construct confidence intervals for penalized spline fits. Due to the penalty, the fitted smooth curve is a biased estimate…

Numerical simulations of physical systems exhibit discrepancies arising from unmodeled physics and idealizations, as well as numerical approximation errors stemming from discretization and solver tolerances. This article reviews techniques…

Physics-informed neural networks (PINNs) have emerged as an effective technique for solving PDEs in a wide range of domains. It is noticed, however, the performance of PINNs can vary dramatically with different sampling procedures. For…

Application of Neural Networks to river hydraulics is fledgling, despite the field suffering from data scarcity, a challenge for machine learning techniques. Consequently, many purely data-driven Neural Networks proved to lack predictive…

Few-Shot Class Incremental Learning (FSCIL) is a challenging continual learning task, where limited training examples are available during several learning sessions. To succeed in this task, it is necessary to avoid over-fitting new classes…

A data-driven model augmentation framework, referred to as Weakly-coupled Integrated Inference and Machine Learning (IIML), is presented to improve the predictive accuracy of physical models. In contrast to parameter calibration, this work…

Adversarial attacks pose significant threats to deploying state-of-the-art classifiers in safety-critical applications. Two classes of methods have emerged to address this issue: empirical defences and certified defences. Although certified…