arXiv subjects

Che-Chia Chang

Publications and source records attributed to Che-Chia Chang.

8 recordsLinked to original sources

arXiv2026

Stabilizing Physics-Informed Consistency Models via Structure-Preserving Training

We propose a physics-informed consistency modeling framework for solving partial differential equations (PDEs) via fast, few-step generative inference. We identify a key stability challenge in physics-constrained consistency training, where PDE residuals can drive the model toward trivial or degenerate solutions, degrading the learned data distribution. To address this, we introduce a structure-preserving two-stage training strategy that decouples distribution learning from physics enforcement by freezing the coefficient decoder during physics-informed fine-tuning. We further propose a two-step residual objective that enforces physical consistency on refined, structurally valid generative trajectories rather than noisy single-step predictions. The resulting framework enables stable, high-fidelity inference for both unconditional generation and forward problems. We demonstrate that forward solutions can be obtained via a projection-based zero-shot inpainting procedure, achieving consistent accuracy of diffusion baselines with orders of magnitude reduction in computational cost.

cs.LG↗

arXiv2026

TINNs: Time-Induced Neural Networks for Solving Time-Dependent PDEs

Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere in space and time. However, standard space-time PINNs take time as an input but reuse a single network with shared weights across all times, forcing the same features to represent markedly different dynamics. This coupling degrades error performance and can destabilize training when enforcing PDE, boundary, and initial constraints jointly. We propose Time-Induced Neural Networks (TINNs), a novel architecture that parameterizes the network weights as a learned function of time, allowing the effective spatial representation to evolve over time while maintaining shared structure. The resulting formulation naturally yields a nonlinear least-squares problem, which we optimize efficiently using a Levenberg-Marquardt method. Experiments on various time-dependent PDEs show up to 4 times improved relative error and 10 times faster convergence compared to PINNs and strong baselines.

cs.LG↗

arXiv2025

Physics-Informed Machine Learning for Two-Phase Moving-Interface and Stefan Problems

The Stefan problem is a classical free-boundary problem that models phase-change processes and poses computational challenges due to its moving interface and nonlinear temperature-phase coupling. In this work, we develop a physics-informed neural network framework for solving two-phase Stefan problems. The proposed method explicitly tracks the interface motion and enforces the discontinuity in the temperature gradient across the interface while maintaining global consistency of the temperature field. Our approach employs two neural networks: one representing the moving interface and the other for the temperature field. The interface network allows rapid categorization of thermal diffusivity in the spatial domain, which is a crucial step for selecting training points for the temperature network. The temperature network's input is augmented with a modified zero-level set function to accurately capture the jump in its normal derivative across the interface. Numerical experiments on two-phase dynamical Stefan problems demonstrate the superior accuracy and effectiveness of our proposed method compared with the ones obtained by other neural network methodology in literature. The results indicate that the proposed framework offers a robust and flexible alternative to traditional numerical methods for solving phase-change problems governed by moving boundaries. In addition, the proposed method can capture an unstable interface evolution associated with the Mullins-Sekerka instability.

physics.comp-ph↗

arXiv2025

Consistency Training with Physical Constraints

We propose a physics-aware Consistency Training (CT) method that accelerates sampling in Diffusion Models with physical constraints. Our approach leverages a two-stage strategy: (1) learning the noise-to-data mapping via CT, and (2) incorporating physics constraints as a regularizer. Experiments on toy examples show that our method generates samples in a single step while adhering to the imposed constraints. This approach has the potential to efficiently solve partial differential equations (PDEs) using deep generative modeling.

cs.LG↗

arXiv2023

A hybrid neural-network and MAC scheme for Stokes interface problems

In this paper, we present a hybrid neural-network and MAC (Marker-And-Cell) scheme for solving Stokes equations with singular forces on an embedded interface in regular domains. As known, the solution variables (the pressure and velocity) exhibit non-smooth behaviors across the interface so extra discretization efforts must be paid near the interface in order to have small order of local truncation errors in finite difference schemes. The present hybrid approach avoids such additional difficulty. It combines the expressive power of neural networks with the convergence of finite difference schemes to ease the code implementation and to achieve good accuracy at the same time. The key idea is to decompose the solution into singular and regular parts. The neural network learning machinery incorporating the given jump conditions finds the singular part solution, while the standard MAC scheme is used to obtain the regular part solution with associated boundary conditions. The two- and three-dimensional numerical results show that the present hybrid method converges with second-order accuracy for the velocity and first-order accuracy for the pressure, and it is comparable with the traditional immersed interface method in literature.

math.NA↗

arXiv2021

A Shallow Ritz Method for Elliptic Problems with Singular Sources

In this paper, a shallow Ritz-type neural network for solving elliptic equations with delta function singular sources on an interface is developed. There are three novel features in the present work; namely, (i) the delta function singularity is naturally removed, (ii) level set function is introduced as a feature input, (iii) it is completely shallow, comprising only one hidden layer. We first introduce the energy functional of the problem and then transform the contribution of singular sources to a regular surface integral along the interface. In such a way, the delta function singularity can be naturally removed without introducing a discrete one that is commonly used in traditional regularization methods, such as the well-known immersed boundary method. The original problem is then reformulated as a minimization problem. We propose a shallow Ritz-type neural network with one hidden layer to approximate the global minimizer of the energy functional. As a result, the network is trained by minimizing the loss function that is a discrete version of the energy. In addition, we include the level set function of the interface as a feature input of the network and find that it significantly improves the training efficiency and accuracy. We perform a series of numerical tests to show the accuracy of the present method and its capability for problems in irregular domains and higher dimensions.

math.NA↗

arXiv2020

SLIM: Simultaneous Logic-in-Memory Computing Exploiting Bilayer Analog OxRAM Devices

Von Neumann architecture based computers isolate/physically separate computation and storage units i.e. data is shuttled between computation unit (processor) and memory unit to realize logic/ arithmetic and storage functions. This to-and-fro movement of data leads to a fundamental limitation of modern computers, known as the memory wall. Logic in-Memory (LIM) approaches aim to address this bottleneck by computing inside the memory units and thereby eliminating the energy-intensive and time-consuming data movement. However, most LIM approaches reported in literature are not truly "simultaneous" as during LIM operation the bitcell can be used only as a Memory cell or only as a Logic cell. The bitcell is not capable of storing both the Memory/Logic outputs simultaneously. Here, we propose a novel 'Simultaneous Logic in-Memory' (SLIM) methodology that allows to implement both Memory and Logic operations simultaneously on the same bitcell in a non-destructive manner without losing the previously stored Memory state. Through extensive experiments we demonstrate the SLIM methodology using non-filamentary bilayer analog OxRAM devices with NMOS transistors (2T-1R bitcell). Detailed programming scheme, array level implementation and controller architecture are also proposed. Furthermore, to study the impact of introducing SLIM array in the memory hierarchy, a simple image processing application (edge detection) is also investigated. It has been estimated that by performing all computations inside the SLIM array, the total Energy Delay Product (EDP) reduces by ~ 40x in comparison to a modern-day computer. EDP saving owing to reduction in data transfer between CPU Memory is observed to be ~ 780x.

cs.ET↗

arXiv2017

Mitigating Asymmetric Nonlinear Weight Update Effects in Hardware Neural Network based on Analog Resistive Synapse

Asymmetric nonlinear weight update is considered as one of the major obstacles for realizing hardware neural networks based on analog resistive synapses because it significantly compromises the online training capability. This paper provides new solutions to this critical issue through co-optimization with the hardware-applicable deep-learning algorithms. New insights on engineering activation functions and a threshold weight update scheme effectively suppress the undesirable training noise induced by inaccurate weight update. We successfully trained a two-layer perceptron network online and improved the classification accuracy of MNIST handwritten digit dataset to 87.8/94.8% by using 6-bit/8-bit analog synapses, respectively, with extremely high asymmetric nonlinearity.

cs.LG↗