相关论文: Towards Stability of Autoregressive Neural Operato…

Autoregressive surrogate models (or \textit{emulators}) of spatiotemporal systems provide an avenue for fast, approximate predictions, with broad applications across science and engineering. At inference time, however, these models are…

Neural network controllers have become popular in control tasks thanks to their flexibility and expressivity. Stability is a crucial property for safety-critical dynamical systems, while stabilization of partially observed systems, in many…

Inverse problems in fluid dynamics are ubiquitous in science and engineering, with applications ranging from electronic cooling system design to ocean modeling. We propose a general and robust approach for solving inverse problems in the…

Recurrent neural networks are capable of learning the dynamics of an unknown nonlinear system purely from input-output measurements. However, the resulting models do not provide any stability guarantees on the input-output mapping. In this…

Time series forecasting has become a critical task due to its high practicality in real-world applications such as traffic, energy consumption, economics and finance, and disease analysis. Recent deep-learning-based approaches have shown…

Neural operators aim to approximate the solution operator of a system of differential equations purely from data. They have shown immense success in modeling complex dynamical systems across various domains. However, the occurrence of…

The goal of this work is to train a neural network which approximates solutions to the Navier-Stokes equations across a region of parameter space, in which the parameters define physical properties such as domain shape and boundary…

Models based on neural networks and machine learning are seeing a rise in popularity in space physics. In particular, the forecasting of geomagnetic indices with neural network models is becoming a popular field of study. These models are…

Coastal regions and river floodplains are particularly vulnerable to the impacts of extreme weather events. Accurate real-time forecasting of hydrodynamic processes in these areas is essential for infrastructure planning and climate…

The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based…

Long-term fluid dynamics forecasting is a critically important problem in science and engineering. While neural operators have emerged as a promising paradigm for modeling systems governed by partial differential equations (PDEs), they…

Accurate long-range prediction of geophysical systems is difficult due to strongly nonlinear dynamics, the high computational cost of full-physics simulations, and the error accumulation that arise when one-step autoregressive surrogates…

In the design of engineered components, rigorous vibration testing is essential for performance validation and identification of resonant frequencies and amplitudes encountered during operation. Performing this evaluation numerically via…

Classical methods of solving spatiotemporal dynamical systems include statistical approaches such as autoregressive integrated moving average, which assume linear and stationary relationships between systems' previous outputs. Development…

Although neural operators are widely used in data-driven physical simulations, their training remains computationally expensive. Recent advances address this issue via downstream learning, where a model pretrained on simpler problems is…

Learning robust and generalizable world models is crucial for enabling efficient and scalable robotic control in real-world environments. In this work, we introduce a novel framework for learning world models that accurately capture…

This work establishes the first rigorous stability guarantees for approximate predictors in delay-adaptive control of nonlinear systems, addressing a key challenge in practical implementations where exact predictors are unavailable. We…

Stability guarantees are crucial when ensuring a fully autonomous robot does not take undesirable or potentially harmful actions. Unfortunately, global stability guarantees are hard to provide in dynamical systems learned from data,…

Recent research shows that supervised learning can be an effective tool for designing near-optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of neural network controllers is still not well…

Current time-series forecasting models are primarily based on transformer-style neural networks. These models achieve long-term forecasting mainly by scaling up the model size rather than through genuinely autoregressive (AR) rollout. From…