Related papers: Incremental Neural Controlled Differential Equatio…

Recurrent neural networks (RNNs) are widely used as a memory model for sequence-related problems. Many variants of RNN have been proposed to solve the gradient problems of training RNNs and process long sequences. Although some classical…

The presented work demonstrates the training of recurrent neural networks (RNNs) from distributions of atom coordinates in solid state structures that were obtained using ab initio molecular dynamics (AIMD) simulations. AIMD simulations on…

Traffic flow forecasting is a fundamental research issue for transportation planning and management, which serves as a canonical and typical example of spatial-temporal predictions. In recent years, Graph Neural Networks (GNNs) and…

The high dimensionality of kinetic equations with stochastic parameters poses major computational challenges for uncertainty quantification (UQ). Traditional Monte Carlo (MC) sampling methods, while widely used, suffer from slow convergence…

We explore how neural differential equations (NDEs) may be trained on highly resolved fluid-dynamical models of unresolved scales providing an ideal framework for data-driven parameterizations in climate models. NDEs overcome some of the…

Irregularly measured time series are common in many of the applied settings in which time series modelling is a key statistical tool, including medicine. This provides challenges in model choice, often necessitating imputation or similar…

Neural surrogates for partial differential equations (PDEs) have become popular due to their potential to quickly simulate physics. With a few exceptions, neural surrogates generally treat the forward evolution of time-dependent PDEs as a…

Physics-Informed Neural Networks (PINNs) present a transformative approach for smart grid modeling by integrating physical laws directly into learning frameworks, addressing critical challenges of data scarcity and physical consistency in…

In many environmental applications, recurrent neural networks (RNNs) are often used to model physical variables with long temporal dependencies. However, due to mini-batch training, temporal relationships between training segments within…

Reduced-order models, also known as proxy model or surrogate model, are approximate models that are less computational expensive as opposed to fully descriptive models. With the integration of machine learning, these models have garnered…

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…

This study aims to benchmark candidate strategies for embedding neural network (NN) surrogates in nonlinear model predictive control (NMPC) formulations that are subject to systems described with partial differential equations and that are…

In the whole aircraft structural optimization loop, thermal analysis plays a very important role. But it faces a severe computational burden when directly applying traditional numerical analysis tools, especially when each optimization…

Neural networks are a commonly used approach to replace physical models with computationally cheap surrogates. Parametric uncertainty quantification can be included in training, assuming that an accurate prior distribution of the model…

We present a graph neural network (GNN) based surrogate framework for molecular dynamics simulations that directly predicts atomic displacements and learns the underlying evolution operator of an atomistic system. Unlike conventional…

Simulating the time evolution of physical systems is pivotal in many scientific and engineering problems. An open challenge in simulating such systems is their multi-resolution dynamics: a small fraction of the system is extremely dynamic,…

Neural networks (NNs) are often used as surrogates or emulators of partial differential equations (PDEs) that describe the dynamics of complex systems. A virtually negligible computational cost of such surrogates renders them an attractive…

Surrogate-assistance approaches have long been used in computationally expensive domains to improve the data-efficiency of optimization algorithms. Neuroevolution, however, has so far resisted the application of these techniques because it…

Accurate constitutive models of soft materials are crucial for understanding their mechanical behavior and ensuring reliable predictions in the design process. To this end, scientific machine learning research has produced flexible and…

Continuous-time models are a natural choice for irregular and asynchronous data. A central design choice is how to embed discrete observations into continuous time. Interpolation- and imputation-based embeddings reconstruct a continuous…