基于深度学习的含噪声数据亚扩散问题发现

在高数据污染下同时进行模型发现和状态估计

Simultaneous model discovery and state estimation under high data corruption

本文提出了一种基于稀疏回归的模型发现和状态估计方法，通过统计似然函数和优化算法在高噪声环境下实现高效建模。

Robust Data-Driven Discovery of Partial Differential Equations under Uncertainties

Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing equations is not known as a prior. In addition, significant measurement noise and complex algorithm hyperparameter tuning usually reduces the robustness of existing methods. A robust data-driven method is proposed in this study for identifying the governing Partial Differential Equations (PDEs) of a given system from noisy data. The proposed method is based on…

利用约束柯尔莫哥洛夫 - 阿诺德网络对积分 - 微分方程中的记忆和非局部核进行神经发现

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks

研究从稀疏有噪观测中发现积分 - 微分方程的记忆和非局部核这一逆问题，提出基于可微求解器框架，用约束柯尔莫哥洛夫 - 阿诺德网络参数化并施加物理约束，经训练和符号回归得到表示，实验表明构造约束比软惩罚更具鲁棒性。

Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control

Sparse model identification enables the discovery of nonlinear dynamical systems purely from data; however, this approach is sensitive to noise, especially in the low-data limit. In this work, we leverage the statistical approach of bootstrap aggregating (bagging) to robustify the sparse identification of nonlinear dynamics (SINDy) algorithm. First, an ensemble of SINDy models is identified from subsets of limited and noisy data. The aggregate model statistics are then used to produce inclusion probabilities of the candidate functions, which enables uncertainty quantification and probabilistic…

Discovery of interpretable structural model errors by combining Bayesian sparse regression and data assimilation: A chaotic Kuramoto-Sivashinsky test case

Models of many engineering and natural systems are imperfect. The discrepancy between the mathematical representations of a true physical system and its imperfect model is called the model error. These model errors can lead to substantial differences between the numerical solutions of the model and the state of the system, particularly in those involving nonlinear, multi-scale phenomena. Thus, there is increasing interest in reducing model errors, particularly by leveraging the rapidly growing observational data to understand their physics and sources. Here, we introduce a framework named MEDI…

基于多保真度高斯过程的微分方程稀疏发现

Sparse discovery of differential equations based on multi-fidelity Gaussian process

针对含噪、稀疏及多保真度数据下的微分方程识别难题，提出基于GPR与MFGP的不确定性量化方法，以稳健恢复方程并通过数值实验验证有效性。

面向参数化偏微分方程发现的不确定性惩罚贝叶斯信息准则的适配研究

Adaptation of uncertainty-penalized Bayesian information criterion for parametric partial differential equation discovery

针对含噪场景下传统信息准则易选复杂PDE的问题，提出扩展UBIC准则，结合功率谱密度数据变换与不确定性量化防过拟合，可高效准确发现含参数化PDE，代码开源。

基于物理约束的开放形式偏微分方程在有限和含噪数据下的鲁棒学习

Physics-constrained robust learning of open-form partial differential equations from limited and noisy data

本研究提出一种基于物理约束的框架，通过强化学习引导的混合PDE生成器和交替的发现-嵌入过程，从有限且含噪的数据中鲁棒地揭示非线性动力系统的开放形式偏微分方程。

Noise-aware Physics-informed Machine Learning for Robust PDE Discovery

This work is concerned with discovering the governing partial differential equation (PDE) of a physical system. Existing methods have demonstrated the PDE identification from finite observations but failed to maintain satisfying results against noisy data, partly owing to suboptimal estimated derivatives and found PDE coefficients. We address the issues by introducing a noise-aware physics-informed machine learning (nPIML) framework to discover the governing PDE from data following arbitrary distributions. We propose training a couple of neural networks, namely solver and preselector, in a mul…