physics-informed cnn

Physics-informed convolutional neural networks (PICNNs) suffer from heavy reliance on manual design, poor generalizability, and limited adaptability across diverse partial differential equation (PDE) problems. Method: We propose the first AutoML framework for PICNNs, featuring a two-stage neural architecture search (NAS) that jointly optimizes CNN architectures and physics-informed loss functions. Specifically, we construct a learnable loss-function factor space and residual adjustment operators, and integrate them with a physics-constrained CNN architecture search space. Contribution/Results: This work pioneers co-automated design of both network topology and physical loss components. Evaluated on multiple PDE benchmarks, our method achieves significantly faster convergence, higher prediction accuracy, and superior cross-problem generalization compared to handcrafted PICNNs—effectively addressing the long-standing challenge of coupled optimization between model architecture and physics-based loss functions in physics-driven learning.

This study addresses critical challenges in applying deep learning to scientific computing—namely, poor interpretability, heavy data dependency, and insufficient physical consistency—within physics-based simulation scenarios. We propose a physics-driven AI modeling framework integrating physics-informed loss functions, differentiable simulators, diffusion-based generative models, physics-guided reinforcement learning, and custom neural architectures, implemented via an interactive Jupyter-based experimental platform. Crucially, we pioneer the systematic embedding of physical priors across the entire deep learning pipeline—model formulation, training, and inference—enabling high-fidelity, data-efficient, and verifiable scientific modeling. The resulting methodology is modular, reusable, and immediately deployable, significantly enhancing model generalizability and interpretability. This work establishes a novel paradigm and technical foundation for next-generation scientific foundation models.

This study investigates how loss functions affect model stability and physical consistency in physics-informed deep learning, particularly under enforced stress-equilibrium boundary conditions. We employ a Pix2Pix network to predict stress fields in hyperelastic composite materials and systematically compare multiple physics-constrained loss formulations. To rigorously assess training variability, we propose a multi-epoch training-based perturbation analysis framework. Results demonstrate significant differences across loss functions in convergence behavior, prediction accuracy, and satisfaction of physical constraints; reporting single-run outcomes obscures inherent instability. Crucially, this work is the first to explicitly identify, quantify, and emphasize the critical impact of training stochasticity on the reproducibility and reliability of physics-informed models. We advocate adopting statistical metrics from multiple independent training runs as a standard evaluation protocol—establishing a novel robustness assessment paradigm for physics-informed neural networks (PINNs) and related methods.

This work addresses the differentiability and portability bottlenecks in numerical solving of partial differential equations (PDEs) for incompressible computational fluid dynamics (CFD). Methodologically, it encodes classical PDE discretization schemes directly as analytical, weight-free convolutional layers and integrates Jacobi iteration with a U-Net architecture to realize a differentiable multigrid solver—entirely without training. The key contribution is the first formulation of a traditional CFD solver as an untrained, fully differentiable, and platform-agnostic neural network module. This enables seamless coupling with data-driven components to construct hybrid physics-AI models. Experiments demonstrate high accuracy and efficiency on the convection–diffusion equation, Burgers equation, and incompressible Navier–Stokes equations—matching the precision of established CFD solvers while incurring zero training cost.

This work addresses the lack of a unified understanding of the design principles, applicability, and performance differences between Physics-Informed Neural Networks (PINNs) and Neural Operators (NOs), which hinders the development of reliable data-driven PDE solvers. It proposes the first unified analytical framework that systematically characterizes the design space of both approaches along three dimensions: learning objectives, mechanisms for embedding physical structure, and strategies for computational load distribution. By elucidating the intrinsic connections and fundamental distinctions between these methods, the study not only clarifies the positioning and performance origins of existing techniques but also provides theoretical guidance and novel pathways for designing efficient and robust PDE solvers that effectively integrate physical priors with data-driven learning.

Deep learning models exhibit generalization capabilities in real-world tasks that surpass predictions from classical statistical learning theory, yet the underlying mechanisms remain poorly understood. This work addresses this gap by integrating statistical learning theory with physics-inspired priors to systematically analyze neural scaling laws under physically constrained scenarios. It uncovers novel scaling behaviors and explicitly models the interplay between inductive biases and architectural design choices. Leveraging a physics-informed machine learning framework, the study elucidates the statistical mechanisms responsible for the exceptional generalization of deep learning in physics-related tasks, thereby providing theoretical foundations and practical guidance for designing models tailored to scientific computing applications.

This work addresses the challenge that generative models in semiconductor manufacturing often produce physically unrealizable outputs due to neglecting fundamental physical constraints. To overcome this limitation, the authors propose a novel generative AI architecture that intrinsically embeds hard constraints from lithography, transport phenomena, reaction kinetics, and device physics, eliminating the need for post-hoc filtering. The framework innovatively integrates four complementary paradigms: physics-informed diffusion models, PDE-constrained variational autoencoders, neural operator priors, and conservation-law-compliant generative networks. This integrated approach enables efficient synthesis of high-fidelity, physically valid masks, layouts, defect patterns, and process recipes, thereby advancing differentiable simulation and autonomous experimentation in semiconductor fabrication.

This work addresses the "black-box" nature of convolutional neural networks (CNNs) in solving image inverse problems by proposing LE-MMSE, the first analytically tractable theoretical framework that explicitly incorporates CNN inductive biases. Built upon minimum mean square error (MMSE) estimation, LE-MMSE formally integrates translation equivariance and local receptive field constraints to yield an interpretable and solvable inverse problem model. Theoretical analysis elucidates the fundamental distinction between physics-aware and physics-agnostic estimators and clarifies the role of high-density regions in the training distribution. Extensive experiments across diverse inverse problems, datasets, and mainstream architectures—including U-Net, ResNet, and PatchMLP—demonstrate remarkable alignment between theoretical predictions and actual CNN outputs, achieving PSNR values consistently above 25 dB, thereby validating the effectiveness and broad applicability of the LE-MMSE framework.

This work addresses the ill-posed nature of microscopic image segmentation, which suffers from noise, weak boundaries, and scarce annotations, leading to poor generalization and unstable solutions in conventional deep learning approaches. The authors propose formulating segmentation as a PDE-constrained optimization problem, uniquely embedding physical priors—specifically reaction-diffusion dynamics and phase-field interfacial energy—as differentiable regularizers within a UNet architecture. This yields a composite objective function that jointly optimizes data fidelity and PDE residual loss. Trained end-to-end, the resulting physics-informed neural segmentation framework achieves significantly improved accuracy and boundary fidelity on the LIVECell dataset, outperforming unconstrained baselines especially in cross-cell-type generalization and few-shot scenarios. The approach effectively bridges the gap between variational methods, statistical learning, and scientific machine learning.