Physics-Informed Uncertainty Enables Reliable AI-driven Design

TL;DR

This work tackles the reliability gap of data-driven surrogates in high-dimensional inverse design by introducing Physics-Informed Uncertainty as a cheap proxy for predictive uncertainty. Applied to frequency-selective surface metasurfaces in the 20–30 GHz range, the approach integrates physics-based uncertainty with multi-fidelity, uncertainty-aware optimization to dramatically improve design success rates and cut computational costs. The results show that uncertainty-guided workflows outperform baseline surrogate-only methods, with multi-fidelity strategies achieving comparable outcomes to full high-fidelity evaluations but at roughly an order of magnitude lower runtime. The study highlights a generalizable framework where physical laws constrain and quantify surrogate trust, offering a path toward robust, autonomous AI-driven scientific discovery across complex, data-limited domains.

Abstract

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.

Figures (15)

• Figure 1: Illustration of how a single-fidelity surrogate-assisted optimization workflow may lead to erroneous designs as the design deviates from its' training distribution whereas an uncertainty-aware multi-fidelity workflow efficiently utilizes high-fidelity evaluations in balancing 'exploration' and 'exploitation' for robust design optimization. The novel aspect of this work is the validation of physics-based rules as an effective uncertainty metric in this real-world problem of metasurface design.
• Figure 2: (a) Illustration of how a periodic arrangement of a meta-atom is frequently used to construct a frequency-selective surface and other useful devices. Segment in the red box is the periodic meta-atom. (b) and (c) represent different possible designs that can be constructed via an 18×18 or 36×36 pixel discretization of the design space of a meta-atom.
• Figure 3: (a) Illustration of 6 examples of (a) input design and their corresponding (b) S-parameter responses and the (c) Transmission (in dB) within the 20 - 30 GHz spectrum.
• Figure 4: (a) Schematic of the WideResNet architecture that was used for the prediction of S-parameter responses based on the input matrices. (b) Illustration of the operations within each group illustrated in (a).
• Figure 5: Band-pass and band-stop profiles and the distributions of training set HF-DES-MAE with respect to the profiles