Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations

Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs). However, purely data-driven models often require extensive training data and can generalize poorly, especially in small-data regimes and under unseen (out-of-distribution) input functions that are not represented in the training data. To address these limitations, we propose the Physics-Informed Laplace Neural Operator (PILNO), which enhances the Laplace Neural Operator (LNO) by embedding governing physics into training through PDE, boundary condition, and initial condition residuals. To improve expressivity, we first introduce an Advanced LNO (ALNO) backbone that retains a pole-residue transient representation while replacing the steady-state branch with an FNO-style Fourier multiplier. To make physics-informed training both data-efficient and robust, PILNO further leverages (i) virtual inputs: an unlabeled ensemble of input functions spanning a broad spectral range that provides abundant physics-only supervision and explicitly targets out-of-distribution (OOD) regimes; and (ii) temporal-causality weighting: a time-decaying reweighting of the physics residual that prioritizes early-time dynamics and stabilizes optimization for time-dependent PDEs. Across four representative benchmarks -- Burgers' equation, Darcy flow, a reaction-diffusion system, and a forced KdV equation -- PILNO consistently improves accuracy in small-data settings (e.g., N_train <= 27), reduces run-to-run variability across random seeds, and achieves stronger OOD generalization than purely data-driven baselines.

EchoScan: Scanning Complex Indoor Geometries via Acoustic Echoes

Accurate estimation of indoor space geometries is vital for constructing precise digital twins, whose broad industrial applications include navigation in unfamiliar environments and efficient evacuation planning, particularly in low-light conditions. This study introduces EchoScan, a deep neural network model that utilizes acoustic echoes to perform room geometry inference. Conventional sound-based techniques rely on estimating geometry-related room parameters such as wall position and room size, thereby limiting the diversity of inferable room geometries. Contrarily, EchoScan overcomes this limitation by directly inferring room floorplans and heights, thereby enabling it to handle rooms with arbitrary shapes, including curved walls. The key innovation of EchoScan is its ability to analyze the complex relationship between low- and high-order reflections in room impulse responses (RIRs) using a multi-aggregation module. The analysis of high-order reflections also enables it to infer complex room shapes when echoes are unobservable from the position of an audio device. Herein, EchoScan was trained and evaluated using RIRs synthesized from complex environments, including the Manhattan and Atlanta layouts, employing a practical audio device configuration compatible with commercial, off-the-shelf devices. Compared with vision-based methods, EchoScan demonstrated outstanding geometry estimation performance in rooms with various shapes.

Ensemble Transfer Learning of Elastography and B-mode Breast Ultrasound Images

Computer-aided detection (CAD) of benign and malignant breast lesions becomes increasingly essential in breast ultrasound (US) imaging. The CAD systems rely on imaging features identified by the medical experts for their performance, whereas deep learning (DL) methods automatically extract features from the data. The challenge of the DL is the insufficiency of breast US images available to train the DL models. Here, we present an ensemble transfer learning model to classify benign and malignant breast tumors using B-mode breast US (B-US) and strain elastography breast US (SE-US) images. This model combines semantic features from AlexNet & ResNet models to classify benign from malignant tumors. We use both B-US and SE-US images to train the model and classify the tumors. We retrospectively gathered 85 patients' data, with 42 benign and 43 malignant cases confirmed with the biopsy. Each patient had multiple B-US and their corresponding SE-US images, and the total dataset contained 261 B-US images and 261 SE-US images. Experimental results show that our ensemble model achieves a sensitivity of 88.89% and specificity of 91.10%. These diagnostic performances of the proposed method are equivalent to or better than manual identification. Thus, our proposed ensemble learning method would facilitate detecting early breast cancer, reliably improving patient care.