Related papers: Active Learning for Neural PDE Solvers
We investigate neural ordinary and stochastic differential equations (neural ODEs and SDEs) to model stochastic dynamics in fully and partially observed environments within a model-based reinforcement learning (RL) framework. Through a…
Unveiling the underlying governing equations of nonlinear dynamic systems remains a significant challenge. Insufficient prior knowledge hinders the determination of an accurate candidate library, while noisy observations lead to imprecise…
In recent years, deep learning has become a breakthrough technique in assisting medical image diagnosis. Supervised learning using convolutional neural networks (CNN) provides state-of-the-art performance and has served as a benchmark for…
Neural operators (NOs) provide a new paradigm for efficiently solving partial differential equations (PDEs), but their training depends on costly high-fidelity data from numerical solvers, limiting applications in complex systems. We…
Pretraining neural networks with massive unlabeled datasets has become popular as it equips the deep models with a better prior to solve downstream tasks. However, this approach generally assumes that the downstream tasks have access to…
Fast and accurate solutions of time-dependent partial differential equations (PDEs) are of pivotal interest to many research fields, including physics, engineering, and biology. Generally, implicit/semi-implicit schemes are preferred over…
Neural operators have recently grown in popularity as Partial Differential Equation (PDE) surrogate models. Learning solution functionals, rather than functions, has proven to be a powerful approach to calculate fast, accurate solutions to…
Recent work has shown that reinforcement learning (RL) is a promising approach to control dynamical systems described by partial differential equations (PDE). This paper shows how to use RL to tackle more general PDE control problems that…
The active learning (AL) technique, one of the state-of-the-art methods for constructing surrogate models, has shown high accuracy and efficiency in forward uncertainty quantification (UQ) analysis. This paper provides a comprehensive study…
Partial differential equations (PDEs) are often computationally challenging to solve, and in many settings many related PDEs must be be solved either at every timestep or for a variety of candidate boundary conditions, parameters, or…
Active learning (AL) algorithms may achieve better performance with fewer data because the model guides the data selection process. While many algorithms have been proposed, there is little study on what the optimal AL algorithm looks like,…
Machine learning (ML) models have emerged as a promising approach for solving partial differential equations (PDEs) in science and engineering. Previous ML models typically cannot generalize outside the training data; for example, a trained…
Active automata learning (AAL) algorithms can learn a behavioral model of a system from interacting with it. The primary challenge remains scaling to larger models, in particular in the presence of many possible inputs to the system. Modern…
Industrial design evaluation often relies on high-fidelity simulations of governing partial differential equations (PDEs). While accurate, these simulations are computationally expensive, making dense exploration of design spaces…
We consider a general class of nonsmooth optimal control problems with partial differential equation (PDE) constraints, which are very challenging due to its nonsmooth objective functionals and the resulting high-dimensional and…
This paper studies a new problem, \emph{active learning with partial labels} (ALPL). In this setting, an oracle annotates the query samples with partial labels, relaxing the oracle from the demanding accurate labeling process. To address…
Data-driven discovery of partial differential equations (PDEs) has attracted increasing attention in recent years. Although significant progress has been made, certain unresolved issues remain. For example, for PDEs with high-order…
Active learning (AL) is a principled strategy to reduce annotation cost in data-hungry deep learning. However, existing AL algorithms focus almost exclusively on unimodal data, overlooking the substantial annotation burden in multimodal…
Hard optimisation problems such as Boolean Satisfiability typically have long solving times and can usually be solved by many algorithms, although the performance can vary widely in practice. Research has shown that no single algorithm…
Increasingly more research areas rely on machine learning methods to accelerate discovery while saving resources. Machine learning models, however, usually require large datasets of experimental or computational results, which in certain…