Physics-Informed ML

Physics-Informed Neural Networks (PINNs) have gained attention for solving partial differential equations, including the scattered Helmholtz equation, due to their flexibility and mesh-free formulation. However, their performance suffers from low-frequency bias, particularly in high-frequency wavefield simulations, limiting convergence speed and accuracy. To address this, we propose a novel and simplified PINN framework that incorporates explicit, trainable Gabor basis functions to efficiently capture the localized and oscillatory nature of wavefields. Unlike previous Gabor-based PINNs that rely on multiplicative filters or auxiliary networks to learn Gabor parameters, our approach redefines the network's task as learning a nonlinear mapping from input coordinates to a custom Gabor coordinate system, where a Gabor function captures the dominant oscillatory behavior of the wavefield. This formulation absorbs the effect of two Gabor parameters into the learned mapping, reducing computational complexity and eliminating the need for manual tuning of hyperparameters. We also present an efficient formulation for incorporating a Perfectly Matched Layer (PML) into the training by deriving real-valued loss components and introducing an analytical expression for the background wavefield. Numerical experiments on various velocity models show that our Gabor-PINN achieves faster convergence, higher accuracy, and greater robustness to architectural design and initialization compared to both traditional PINNs and prior Gabor-based methods. The improvement lies not in adding architectural complexity --as is common in enhanced PINNs -- but in absorbing this complexity into the learned coordinate transformation, making the method both simpler and more effective. Our implementation is publicly available to support reproducibility and future research.

Kernel selection for regression of physical observables is often heuristic. We investigate a physics-informed strategy in which functional forms and spectral structures associated with Green's functions motivate kernel selection without requiring an exact identification between a machine-learning kernel and a physical propagator. The principal construction is a Jackson-damped Chebyshev kernel inspired by the kernel polynomial method (KPM); its explicit feature map yields a positive-semidefinite Gram matrix by construction and provides an inspectable spectral prior for structured observables. We evaluate standard and custom SVR models on copper-conductivity proxies, local Dirac-like band dispersion, quartic-oscillator energy levels, photonic-crystal transmission, and Fibonacci-chain transmission using repeated nested validation, learning curves, random-forest and multilayer-perceptron baselines, and low-rank Nyström tests where relevant. The framework is intended for finite-data regression of precomputed observables while boundary conditions remain part of the physical model that generates those observables.

Gate-defined semiconductor quantum-dot (QD) arrays are a promising platform for quantum computing. However, their large configuration spaces and inherent measurement noise make device tuning time consuming and difficult to scale. Although machine-learning (ML) approaches for automated tuning have proliferated rapidly, a fair comparison of methods remains limited by inconsistent metrics and a lack of standardized labeled datasets. Here, we introduce Geometry-Informed ANNotator for Electrostatic Topologies (GAnnET), a physics- and geometry-informed algorithm that automatically generates probabilistic state labels for charge stability diagrams (CSDs) of double-QD systems. GAnnET constructs local geometric models of CSD structure and combines them into a global state map with calibrated confidence, eliminating the need for manual annotation. We validate GAnnET on simulated and experimental CSDs and demonstrate consistent labeling suitable for ML training and benchmarking. By enabling reproducible annotation of experimental data, GAnnET supports community benchmarking and scalable automated QD operation.