Inverse problems describe the task of recovering an underlying signal of interest given observables. Typically, the observables are related via some non-linear forward model applied to the underlying unknown signal. Inverting the non-linear forward model can be computationally expensive, as it often involves computing and inverting a linearization at a series of estimates. Rather than inverting the physics-based model, we instead train a surrogate forward model (emulator) and leverage modern auto-grad libraries to solve for the input within a classical optimization framework. Current methods to train emulators are done in a black box supervised machine learning fashion and fail to take advantage of any existing knowledge of the forward model. In this article, we propose a simple learned weighted average model that embeds linearizations of the forward model around various reference points into the model itself, explicitly incorporating known physics. Grounding the learned model with physics based linearizations improves the forward modeling accuracy and provides richer physics based gradient information during the inversion process leading to more accurate signal recovery. We demonstrate the efficacy on an ocean acoustic tomography (OAT) example that aims to recover ocean sound speed profile (SSP) variations from acoustic observations (e.g. eigenray arrival times) within simulation of ocean dynamics in the Gulf of Mexico.

翻译：反问题描述的是根据观测数据恢复潜在目标信号的任务。通常，观测值通过某种非线性前向模型与未知目标信号相关联。对非线性前向模型求逆的计算成本较高，往往需要在一系列估计值处计算并求逆线性化模型。本文不直接对基于物理的模型求逆，而是训练替代前向模型（仿真器），并利用现代自动求导库在经典优化框架中求解输入信号。现有的仿真器训练方法采用黑箱式监督机器学习方式，未能充分利用前向模型的已有知识。本文提出一种简单的加权平均学习模型，将前向模型在不同参考点处的线性化结构嵌入模型自身，显式融入已知物理知识。基于物理线性化的学习模型可提升前向建模精度，并在反演过程中提供更丰富的基于物理的梯度信息，从而更精确地恢复信号。我们通过墨西哥湾海洋动力学仿真中的声学海洋层析成像（OAT）示例验证了该方法的有效性，该示例旨在根据声学观测数据（如本征声线到达时间）恢复海洋声速剖面（SSP）变化。