Seungchul Lee

Heechang Kim, Qianying Cao, Hyomin Shin et al.

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.

Sampa Misra, Seungwan Jeon, Ravi Managuli et al.

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.