Analysis of Truncated Singular Value Decomposition for Koopman Operator-Based Lane Change Model

• URL: http://arxiv.org/abs/2409.18586v1
• Date: Fri, 27 Sep 2024 09:45:21 GMT
• Title: Analysis of Truncated Singular Value Decomposition for Koopman Operator-Based Lane Change Model
• Authors: Chinnawut Nantabut,
• Abstract summary: Singular Value Decomposition (SVD) is employed to approximate Koopman operators from extensive datasets efficiently. This study evaluates different basis functions used in EDMD and ranks for truncated SVD for representing lane change behavior models. The findings, however, suggest that the technique of truncated SVD does not necessarily achieve substantial reductions in computational training time and results in significant information loss.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Understanding and modeling complex dynamic systems is crucial for enhancing vehicle performance and safety, especially in the context of autonomous driving. Recently, popular methods such as Koopman operators and their approximators, known as Extended Dynamic Mode Decomposition (EDMD), have emerged for their effectiveness in transforming strongly nonlinear system behavior into linear representations. This allows them to be integrated with conventional linear controllers. To achieve this, Singular Value Decomposition (SVD), specifically truncated SVD, is employed to approximate Koopman operators from extensive datasets efficiently. This study evaluates different basis functions used in EDMD and ranks for truncated SVD for representing lane change behavior models, aiming to balance computational efficiency with information loss. The findings, however, suggest that the technique of truncated SVD does not necessarily achieve substantial reductions in computational training time and results in significant information loss.

Related papers

• Koopman AutoEncoder via Singular Value Decomposition for Data-Driven Long-Term Prediction [31.853422606200382]
  Controlling eigenvalues is challenging due to high computational complexity and difficulties in managing them during the training process. We propose leveraging the singular value decomposition (SVD) of the Koopman matrix to adjust the singular values for better long-term prediction. Experimental results demonstrate that, during training, the loss term for singular values effectively brings the eigenvalues close to the unit circle, and the proposed approach outperforms existing baseline methods for long-term prediction tasks.
  arXiv  Detail & Related papers  (2024-08-21T03:15:37Z)
• Sobolev neural network with residual weighting as a surrogate in linear and non-linear mechanics [0.0]
  This paper investigates the improvement of the training process by including sensitivity information. In computational mechanics, sensitivities can be applied to neural networks by expanding the training loss function. This improvement is shown in two examples of linear and non-linear material behavior.
  arXiv  Detail & Related papers  (2024-07-23T13:28:07Z)
• DeltaPhi: Learning Physical Trajectory Residual for PDE Solving [54.13671100638092]
  We propose and formulate the Physical Trajectory Residual Learning (DeltaPhi) We learn the surrogate model for the residual operator mapping based on existing neural operator networks. We conclude that, compared to direct learning, physical residual learning is preferred for PDE solving.
  arXiv  Detail & Related papers  (2024-06-14T07:45:07Z)
• Large-Scale OD Matrix Estimation with A Deep Learning Method [70.78575952309023]
  The proposed method integrates deep learning and numerical optimization algorithms to infer matrix structure and guide numerical optimization. We conducted tests to demonstrate the good generalization performance of our method on a large-scale synthetic dataset.
  arXiv  Detail & Related papers  (2023-10-09T14:30:06Z)
• Koopman Kernel Regression [6.116741319526748]
  We show that Koopman operator theory offers a beneficial paradigm for characterizing forecasts via linear time-invariant (LTI) ODEs. We derive a universal Koopman-invariant kernel reproducing Hilbert space (RKHS) that solely spans transformations into LTI dynamical systems. Our experiments demonstrate superior forecasting performance compared to Koopman operator and sequential data predictors.
  arXiv  Detail & Related papers  (2023-05-25T16:22:22Z)
• End-to-End Meta-Bayesian Optimisation with Transformer Neural Processes [52.818579746354665]
  This paper proposes the first end-to-end differentiable meta-BO framework that generalises neural processes to learn acquisition functions via transformer architectures. We enable this end-to-end framework with reinforcement learning (RL) to tackle the lack of labelled acquisition data.
  arXiv  Detail & Related papers  (2023-05-25T10:58:46Z)
• On Robust Numerical Solver for ODE via Self-Attention Mechanism [82.95493796476767]
  We explore training efficient and robust AI-enhanced numerical solvers with a small data size by mitigating intrinsic noise disturbances. We first analyze the ability of the self-attention mechanism to regulate noise in supervised learning and then propose a simple-yet-effective numerical solver, Attr, which introduces an additive self-attention mechanism to the numerical solution of differential equations.
  arXiv  Detail & Related papers  (2023-02-05T01:39:21Z)
• Physics-guided Data Augmentation for Learning the Solution Operator of Linear Differential Equations [2.1850269949775663]
  We propose a physics-guided data augmentation (PGDA) method to improve the accuracy and generalization of neural operator models. We demonstrate the advantage of PGDA on a variety of linear differential equations, showing that PGDA can improve the sample complexity and is robust to distributional shift.
  arXiv  Detail & Related papers  (2022-12-08T06:29:15Z)
• Automatic Data Augmentation via Invariance-Constrained Learning [94.27081585149836]
  Underlying data structures are often exploited to improve the solution of learning tasks. Data augmentation induces these symmetries during training by applying multiple transformations to the input data. This work tackles these issues by automatically adapting the data augmentation while solving the learning task.
  arXiv  Detail & Related papers  (2022-09-29T18:11:01Z)
• How robust are pre-trained models to distribution shift? [82.08946007821184]
  We show how spurious correlations affect the performance of popular self-supervised learning (SSL) and auto-encoder based models (AE) We develop a novel evaluation scheme with the linear head trained on out-of-distribution (OOD) data, to isolate the performance of the pre-trained models from a potential bias of the linear head used for evaluation.
  arXiv  Detail & Related papers  (2022-06-17T16:18:28Z)
• Derivative-Based Koopman Operators for Real-Time Control of Robotic Systems [14.211417879279075]
  This paper presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error. We construct a Koopman operator-based linear representation and utilize Taylor series accuracy analysis to derive an error bound. When combined with control, the Koopman representation of the nonlinear system has marginally better performance than competing nonlinear modeling methods.
  arXiv  Detail & Related papers  (2020-10-12T15:15:13Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.