用于从图像学习连续潜在动力学模型的保连续性卷积自编码器
Continuity-Preserving Convolutional Autoencoders for Learning Continuous Latent Dynamical Models from Images
AI总结：
本文提出保连续性卷积自编码器（CpAEs），通过促进卷积滤波器连续性来保持潜在状态连续，从而从离散图像帧中学习更准确的连续潜在动力学模型。
摘要：
连续动力系统是许多科学与工程学科的基石。尽管机器学习提供了从轨迹数据建模这些系统的强大工具，但当这些轨迹以图像形式捕获时，就会产生本质上是离散的像素级观测，从而带来挑战。因此，直接应用卷积自编码器可能导致潜在坐标在时间上不连续。为解决这一问题，我们提出了保连续性卷积自编码器（CpAEs），用于从离散图像帧中学习连续潜在状态及其对应的连续潜在动力学模型。我们给出了从图像帧学习动力学的数学表述，说明了以往方法存在的问题，并基于促进卷积滤波器的连续性来保持潜在状态的连续性，从而引出我们的方法。该方法使CpAEs能够产生随底层动力学连续演化的潜在状态，从而得到更准确的潜在动力学模型。在多种场景下的大量实验证明了CpAEs的有效性。
英文摘要：
Continuous dynamical systems are cornerstones of many scientific and engineering disciplines. While machine learning offers powerful tools to model these systems from trajectory data, challenges arise when these trajectories are captured as images, resulting in pixel-level observations that are discrete in nature. Consequently, a naive application of a convolutional autoencoder can result in latent coordinates that are discontinuous in time. To resolve this, we propose continuity-preserving convolutional autoencoders (CpAEs) to learn continuous latent states and their corresponding continuous latent dynamical models from discrete image frames. We present a mathematical formulation for learning dynamics from image frames, which illustrates issues with previous approaches and motivates our methodology based on promoting the continuity of convolution filters, thereby preserving the continuity of the latent states. This approach enables CpAEs to produce latent states that evolve continuously with the underlying dynamics, leading to more accurate latent dynamical models. Extensive experiments across various scenarios demonstrate the effectiveness of CpAEs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
