Related papers: Residual Koopman Spectral Profiling for Predicting…

This work determines the inaccuracy of using Reynolds averaged Navier Stokes (RANS) turbulence models in transition to turbulent flow regimes by predicting the model-based discrepancies between RANS and large eddy simulation (LES) models…

Koopman decomposition is a non-linear generalization of eigen-decomposition, and is being increasingly utilized in the analysis of spatio-temporal dynamics. Well-known techniques such as the dynamic mode decomposition (DMD) and its linear…

Reinforcement learning (RL) has been widely applied to dynamic routing, modulation and spectrum assignment (RMSA) in optical networks, yet no prior work has trained a transformer model for this task. We attribute this to the high data and…

This paper proposes an adaptive near-field beam training method to enhance performance in multi-user and multipath environments. The approach identifies multiple strongest beams through beam sweeping and linearly combines their received…

Reliable estimation of contact forces is crucial for ensuring safe and precise interaction of robots with unstructured environments. However, accurate sensorless force estimation remains challenging due to inherent modeling errors and…

We investigate the construction of early stopping rules in the nonparametric regression problem where iterative learning algorithms are used and the optimal iteration number is unknown. More precisely, we study the discrepancy principle, as…

Finetuning pretrained models occurs in a low-dimensional subspace of the full parameter space. Prior work has focused on characterizing this optimization subspace, but largely ignored the complementary question: why do certain directions…

While neural networks have made significant strides in many AI tasks, they remain vulnerable to a range of noise types, including natural corruptions, adversarial noise, and low-resolution artifacts. Many existing approaches focus on…

Forecasting multiscale chaotic dynamical systems, such as turbulent flows, with deep learning remains a formidable challenge due to the spectral bias of neural networks, which hinders the accurate representation of fine-scale structures in…

Data-driven spectral analysis of Koopman operators is a powerful tool for understanding numerous real-world dynamical systems, from neuronal activity to variations in sea surface temperature. The Koopman operator acts on a function space…

The ability to identify useful features or representations of the input data based on training data that achieves low prediction error on test data across multiple prediction tasks is considered the key to multitask learning success. In…

This work investigates the detection of instabilities that may occur when utilizing deep learning models for image reconstruction tasks. Although neural networks often empirically outperform traditional reconstruction methods, their usage…

We propose a noise-robust learning framework for the Koopman operator of nonlinear dynamical systems, with guaranteed long-term stability and improved model performance for better model-based predictive control tasks. Unlike some existing…

The Koopman operator provides a powerful framework for representing the dynamics of general nonlinear dynamical systems. However, existing data-driven approaches to learning the Koopman operator rely on batch data. In this work, we present…

Estimating accurate forward and inverse dynamics models is a crucial component of model-based control for sophisticated robots such as robots driven by hydraulics, artificial muscles, or robots dealing with different contact situations.…

With the development of end-to-end control based on deep learning, it is important to study new system modeling techniques to realize dynamics modeling with high-dimensional inputs. In this paper, a novel Koopman-based deep convolutional…

This paper presents a data-driven method to identify an asymptotically stable Koopman system from noisy data. In particular, the proposed approach combines approximations of the system's forward- and backward-in-time dynamics to reduce bias…

Computational color constancy that requires esti- mation of illuminant colors of images is a fundamental yet active problem in computer vision, which can be formulated into a regression problem. To learn a robust regressor for color…

We study the metastability properties of a simple prototypical bistable system using the formalism of the Koopman operator. Instead of studying noise-induced transitions by following the trajectories of the system, we track them by studying…

We present the first systematic study of weight matrix singular value spectra \emph{during} transformer pretraining, tracking full SVD decompositions of every weight matrix at 25-step intervals across three model scales (30M--285M…