Giuseppe Romano

Lu Lu, Raphael Pestourie, Steven G. Johnson et al.

Deep neural operators can learn operators mapping between infinite-dimensional function spaces via deep neural networks and have become an emerging paradigm of scientific machine learning. However, training neural operators usually requires a large amount of high-fidelity data, which is often difficult to obtain in real engineering problems. Here, we address this challenge by using multifidelity learning, i.e., learning from multifidelity datasets. We develop a multifidelity neural operator based on a deep operator network (DeepONet). A multifidelity DeepONet includes two standard DeepONets coupled by residual learning and input augmentation. Multifidelity DeepONet significantly reduces the required amount of high-fidelity data and achieves one order of magnitude smaller error when using the same amount of high-fidelity data. We apply a multifidelity DeepONet to learn the phonon Boltzmann transport equation (BTE), a framework to compute nanoscale heat transport. By combining a trained multifidelity DeepONet with genetic algorithm or topology optimization, we demonstrate a fast solver for the inverse design of BTE problems.

Giuseppe Romano, Rodrigo Arrieta, Steven G. Johnson

A key challenge in topology optimization (TopOpt) is that manufacturable structures, being inherently binary, are non-differentiable, creating a fundamental tension with gradient-based optimization. The subpixel-smoothed projection (SSP) method addresses this issue by smoothing sharp interfaces at the subpixel level through a first-order expansion of the filtered field. However, SSP does not guarantee differentiability under topology changes, such as the merging of two interfaces, and therefore violates the convergence guarantees of many popular gradient-based optimization algorithms. We overcome this limitation by regularizing SSP with the Hessian of the filtered field, resulting in a twice-differentiable projected density during such transitions, while still guaranteeing an almost-everywhere binary structure. We demonstrate the effectiveness of our second-order SSP (SSP2) methodology on both thermal and photonic problems, showing that SSP2 has faster convergence than SSP for connectivity-dominant cases -- where frequent topology changes occur -- while exhibiting comparable performance otherwise. Beyond improving convergence guarantees for CCSA optimizers, SSP2 enables the use of a broader class of optimization algorithms with stronger theoretical guarantees, such as interior-point methods. Since SSP2 adds minimal complexity relative to SSP or traditional projection schemes, it can be used as a drop-in replacement in existing TopOpt codes.

Antonio Varagnolo, Giuseppe Romano, Raphaël Pestourie

Designing materials with controlled heat flow at the nano-scale is central to advances in microelectronics, thermoelectrics, and energy-conversion technologies. At these scales, phonon transport follows the Boltzmann Transport Equation (BTE), which captures non-diffusive (ballistic) effects but is too costly to solve repeatedly in inverse-design loops. Existing surrogate approaches trade speed for accuracy: fast macroscopic solvers can overestimate conductivities by hundreds of percent, while recent data-driven operator learners often require thousands of high-fidelity simulations. This creates a need for a fast, data-efficient surrogate that remains reliable across ballistic and diffusive regimes. We introduce a Physics-Enhanced Deep Surrogate (PEDS) that combines a differentiable Fourier solver with a neural generator and couples it with uncertainty-driven active learning. The Fourier solver acts as a physical inductive bias, while the network learns geometry-dependent corrections and a mixing coefficient that interpolates between macroscopic and nano-scale behavior. PEDS reduces training-data requirements by up to 70% compared with purely data-driven baselines, achieves roughly 5% fractional error with only 300 high-fidelity BTE simulations, and enables efficient design of porous geometries spanning 12-85 W m$^{-1}$ K$^{-1}$ with average design errors of 4%. The learned mixing parameter recovers the ballistic-diffusive transition and improves out of distribution robustness. These results show that embedding simple, differentiable low-fidelity physics can dramatically increase surrogate data-efficiency and interpretability, making repeated PDE-constrained optimization practical for nano-scale thermal-materials design.

Felipe Oviedo, Zekun Ren, Shijing Sun et al.

X-ray diffraction (XRD) data acquisition and analysis is among the most time-consuming steps in the development cycle of novel thin-film materials. We propose a machine-learning-enabled approach to predict crystallographic dimensionality and space group from a limited number of thin-film XRD patterns. We overcome the scarce-data problem intrinsic to novel materials development by coupling a supervised machine learning approach with a model agnostic, physics-informed data augmentation strategy using simulated data from the Inorganic Crystal Structure Database (ICSD) and experimental data. As a test case, 115 thin-film metal halides spanning 3 dimensionalities and 7 space-groups are synthesized and classified. After testing various algorithms, we develop and implement an all convolutional neural network, with cross validated accuracies for dimensionality and space-group classification of 93% and 89%, respectively. We propose average class activation maps, computed from a global average pooling layer, to allow high model interpretability by human experimentalists, elucidating the root causes of misclassification. Finally, we systematically evaluate the maximum XRD pattern step size (data acquisition rate) before loss of predictive accuracy occurs, and determine it to be 0.16°, which enables an XRD pattern to be obtained and classified in 5.5 minutes or less.