Inverse design is a central goal in much of science and engineering, including frequency-selective surfaces (FSS) that are critical to microelectronics for telecommunications and optical metamaterials. Traditional surrogate-assisted optimization methods using deep learning can accelerate the design process but do not usually incorporate uncertainty quantification, leading to poorer optimization performance due to erroneous predictions in data-sparse regions. Here, we introduce and validate a fundamentally different paradigm of Physics-Informed Uncertainty, where the degree to which a model's prediction violates fundamental physical laws serves as a computationally-cheap and effective proxy for predictive uncertainty. By integrating physics-informed uncertainty into a multi-fidelity uncertainty-aware optimization workflow to design complex frequency-selective surfaces within the 20 - 30 GHz range, we increase the success rate of finding performant solutions from less than 10% to over 50%, while simultaneously reducing computational cost by an order of magnitude compared to the sole use of a high-fidelity solver. These results highlight the necessity of incorporating uncertainty quantification in machine-learning-driven inverse design for high-dimensional problems, and establish physics-informed uncertainty as a viable alternative to quantifying uncertainty in surrogate models for physical systems, thereby setting the stage for autonomous scientific discovery systems that can efficiently and robustly explore and evaluate candidate designs.

翻译：逆向设计是科学与工程领域的核心目标之一，涵盖对微电子通信和光学超材料至关重要的频率选择表面。传统基于深度学习的代理辅助优化方法虽能加速设计流程，但通常未纳入不确定性量化，导致在数据稀疏区域因错误预测而降低优化性能。本文提出并验证了一种根本性的新范式——物理信息不确定性，该范式以模型预测违反基本物理定律的程度作为预测不确定性的计算高效且有效的代理指标。通过将物理信息不确定性融入多保真度不确定性感知优化工作流，用于设计20-30 GHz频段内的复杂频率选择表面，我们将获得高性能解决方案的成功率从不足10%提升至50%以上，同时相较于单独使用高保真求解器，计算成本降低了一个数量级。这些结果凸显了在高维问题的机器学习驱动逆向设计中纳入不确定性量化的必要性，并确立了物理信息不确定性作为物理系统代理模型中不确定性量化的可行替代方案，从而为能够高效、稳健地探索和评估候选设计的自主科学发现系统奠定了基础。