Related papers: Probabilistic operator learning: generative modeli…

Bayesian inference on structured models typically relies on the ability to infer posterior distributions of underlying hidden variables. However, inference in implicit models or complex posterior distributions is hard. A popular tool for…

Out-of-distribution (OOD) generalisation is challenging because it involves not only learning from empirical data, but also deciding among various notions of generalisation, e.g., optimising the average-case risk, worst-case risk, or…

We present a system to help designers create icons that are widely used in banners, signboards, billboards, homepages, and mobile apps. Designers are tasked with drawing contours, whereas our system colorizes contours in different styles.…

Imitation learning (IL) provides a data-driven framework for approximating policies for large-scale combinatorial optimisation problems formulated as sequential decision problems (SDPs), where exact solution methods are computationally…

In this work, we introduce implicit Finite Operator Learning (iFOL) for the continuous and parametric solution of partial differential equations (PDEs) on arbitrary geometries. We propose a physics-informed encoder-decoder network to…

In this paper, we investigate the behavior of gradient descent algorithms in physics-informed machine learning methods like PINNs, which minimize residuals connected to partial differential equations (PDEs). Our key result is that the…

We argue that in-context learning (ICL) predictably arises from standard self-supervised next-token pretraining, rather than being an exotic emergent property. This work establishes the foundational principles of this emergence by focusing…

The automated construction of coarse-grained models represents a pivotal component in computer simulation of physical systems and is a key enabler in various analysis and design tasks related to uncertainty quantification. Pertinent methods…

Probabilistic convolutional neural networks, which predict distributions of predictions instead of point estimates, led to recent advances in many areas of computer vision, from image reconstruction to semantic segmentation. Besides state…

In-context learning (ICL) -- the capacity of a model to infer and apply abstract patterns from examples provided within its input -- has been extensively studied in large language models trained for next-token prediction on human text. In…

Approximating nonlinear differential equations using a neural network provides a robust and efficient tool for various scientific computing tasks, including real-time predictions, inverse problems, optimal controls, and surrogate modeling.…

Operator learning enables fast surrogate modeling of high-dimensional dynamical systems, but existing approaches face two fundamental limitations: quadratic inference complexity and unreliable uncertainty quantification in safety-critical…

Operator learning aims to discover properties of an underlying dynamical system or partial differential equation (PDE) from data. Here, we present a step-by-step guide to operator learning. We explain the types of problems and PDEs amenable…

In this work, we explore the mechanism of in-context learning (ICL) on out-of-distribution (OOD) tasks that were not encountered during training. To achieve this, we conduct synthetic experiments where the objective is to learn OOD…

Generative adversarial networks (GANs) provide an algorithmic framework for constructing generative models with several appealing properties: they do not require a likelihood function to be specified, only a generating procedure; they…

This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an…

We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…

Recent years have witnessed a growing call for renewed emphasis on neuroscience-inspired approaches in artificial intelligence research, under the banner of NeuroAI. A prime example of this is predictive coding networks (PCNs), based on the…

In-context learning is a surprising and important phenomenon that emerged when modern language models were scaled to billions of learned parameters. Without modifying a large language model's weights, it can be tuned to perform various…

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…