arXiv subjects

Chuwei Wang

Publications and source records attributed to Chuwei Wang.

11 recordsLinked to original sources

arXiv2026

Toward the Thermodynamic Limit: Neural Operators for Non-equilibrium Dynamics of Mott Insulators

Mott insulators exhibit complex photoexcitation dynamics under intense optical driving, with potential implications for carrier multiplication beyond the Shockley-Queisser limit. Probing these nonequilibrium processes requires access to the thermodynamic limit, where the number of lattice sites becomes arbitrarily large, but conventional solvers are constrained to small systems due to the exponential growth of the Hilbert space. Fourier Neural Operators (FNOs), originally developed for solving partial differential equations, naturally accommodate inputs of varying resolution and are capable of capturing nonlocal effects. Here, we employ FNOs to learn the mapping from noise-perturbed ground-state momentum distributions to their post-pulse counterparts across a range of interaction strengths and driving parameters. Trained only on small lattices, the model generalizes zero-shot to much larger systems, producing physically reasonable momentum distributions well beyond the reach of numerical solvers. Specifically, the model can predict momentum distribution for a 1024x1024 system within a few seconds that matches the theoretical behavior of key observables, whereas direct numerical simulations have so far been restricted to edge sizes of ~30. These results demonstrate the potential of neural operators to directly access large-scale nonequilibrium dynamics, providing a new pathway toward the thermodynamic limit in strongly correlated materials.

cond-mat.str-el↗

arXiv2026

From Vision to Decision: Neuromorphic Control for Autonomous Navigation and Tracking

Robotic navigation has historically struggled to reconcile reactive, sensor-based control with the decisive capabilities of model-based planners. This duality becomes critical when the absence of a predominant option among goals leads to indecision, challenging reactive systems to break symmetries without computationally-intense planners. We propose a parsimonious neuromorphic control framework that bridges this gap for vision-guided navigation and tracking. Image pixels from an onboard camera are encoded as inputs to dynamic neuronal populations that directly transform visual target excitation into egocentric motion commands. A dynamic bifurcation mechanism resolves indecision by delaying commitment until a critical point induced by the environmental geometry. Inspired by recently proposed mechanistic models of animal cognition and opinion dynamics, the neuromorphic controller provides real-time autonomy with a minimal computational burden, a small number of interpretable parameters, and can be seamlessly integrated with application-specific image processing pipelines. We validate our approach in simulation environments as well as on an experimental quadrotor platform.

cs.RO↗

arXiv2025

From Black Hole to Galaxy: Neural Operator: Framework for Accretion and Feedback Dynamics

Modeling how supermassive black holes co-evolve with their host galaxies is notoriously hard because the relevant physics spans nine orders of magnitude in scale-from milliparsecs to megaparsecs--making end-to-end first-principles simulation infeasible. To characterize the feedback from the small scales, existing methods employ a static subgrid scheme or one based on theoretical guesses, which usually struggle to capture the time variability and derive physically faithful results. Neural operators are a class of machine learning models that achieve significant speed-up in simulating complex dynamics. We introduce a neural-operator-based ''subgrid black hole'' that learns the small-scale local dynamics and embeds it within the direct multi-level simulations. Trained on small-domain (general relativistic) magnetohydrodynamic data, the model predicts the unresolved dynamics needed to supply boundary conditions and fluxes at coarser levels across timesteps, enabling stable long-horizon rollouts without hand-crafted closures. Thanks to the great speedup in fine-scale evolution, our approach for the first time captures intrinsic variability in accretion-driven feedback, allowing dynamic coupling between the central black hole and galaxy-scale gas. This work reframes subgrid modeling in computational astrophysics with scale separation and provides a scalable path toward data-driven closures for a broad class of systems with central accretors.

astro-ph.HE↗

arXiv2025

Physics-Aware Neural Operators for Direct Inversion in 3D Photoacoustic Tomography

Learning physics-constrained inverse operators-rather than post-processing physics-based reconstructions-is a broadly applicable strategy for problems with expensive forward models. We demonstrate this principle in three-dimensional photoacoustic computed tomography (3D PACT), where current systems demand dense transducer arrays and prolonged scans, restricting clinical translation. We introduce PANO (PACT imaging neural operator), an end-to-end physics-aware neural operator-a deep learning architecture that generalizes across input sampling densities without retraining-that directly learns the inverse mapping from raw sensor measurements to a 3D volumetric image. Unlike two-step methods that reconstruct then denoise, PANO performs direct inversion in a single pass, jointly embedding physics and data priors. It employs spherical discrete-continuous convolutions to respect hemispherical sensor geometry and Helmholtz equation constraints to ensure physical consistency. PANO reconstructs high-quality images from both simulated and real data across diverse sparse acquisition settings, achieves real-time inference and outperforms the widely-used UBP algorithm by approximately 33 percentage points in cosine similarity on simulated data and 14 percentage points on real phantom data. These results establish a pathway toward more accessible 3D PACT systems for preclinical research, and motivate future in-vivo validation for clinical translation.

eess.IV↗

arXiv2025

EquiReg: Equivariance Regularized Diffusion for Inverse Problems

Diffusion models represent the state-of-the-art for solving inverse problems such as image restoration tasks. Diffusion-based inverse solvers incorporate a likelihood term to guide prior sampling, generating data consistent with the posterior distribution. However, due to the intractability of the likelihood, most methods rely on isotropic Gaussian approximations, which can push estimates off the data manifold and produce inconsistent, poor reconstructions. We propose Equivariance Regularized (EquiReg) diffusion, a general plug-in framework that improves posterior sampling by penalizing trajectories that deviate from the data manifold. EquiReg formalizes manifold-preferential equivariant functions that exhibit low equivariance error for on-manifold samples and high error for off-manifold ones, thereby guiding sampling toward symmetry-preserving regions of the solution space. We highlight that such functions naturally emerge when training non-equivariant models with augmentation or on data with symmetries. EquiReg's largest gains are under reduced sampling and measurement consistency steps, where many methods suffer severe quality degradation. By regularizing trajectories toward the manifold, EquiReg implicitly accelerates convergence and enables high-quality reconstructions. EquiReg consistently improves performance in linear and nonlinear image restoration tasks and solving partial differential equations. Our code is available at https://github.com/Anima-Lab/EquiReg

cs.LG↗

arXiv2024

Coarse Graining with Neural Operators for Simulating Chaotic Systems

Accurately predicting the long-term behavior of chaotic systems is crucial for various applications such as climate modeling. However, achieving such predictions typically requires iterative computations over a dense spatiotemporal grid to account for the unstable nature of chaotic systems, which is expensive and impractical in many real-world situations. An alternative approach to such a full-resolved simulation is using a coarse grid and then correcting its errors through a \textit{closure model}, which approximates the overall information from fine scales not captured in the coarse-grid simulation. Recently, ML approaches have been used for closure modeling, but they typically require a large number of training samples from expensive fully-resolved simulations (FRS). In this work, we prove an even more fundamental limitation, i.e., the standard approach to learning closure models suffers from a large approximation error for generic problems, no matter how large the model is, and it stems from the non-uniqueness of the mapping. We propose an alternative end-to-end learning approach using a physics-informed neural operator (PINO) that overcomes this limitation by not using a closure model or a coarse-grid solver. We first train the PINO model on data from a coarse-grid solver and then fine-tune it with (a small amount of) FRS and physics-based losses on a fine grid. The discretization-free nature of neural operators means that they do not suffer from the restriction of a coarse grid that closure models face, and they can provably approximate the long-term statistics of chaotic systems. In our experiments, our PINO model achieves a 330x speedup compared to FRS with a relative error $\sim 10\%$. In contrast, the closure model coupled with a coarse-grid solver is $60$x slower than PINO while having a much higher error $\sim186\%$ when the closure model is trained on the same FRS dataset.

cs.LG↗

arXiv2024

DOF: Accelerating High-order Differential Operators with Forward Propagation

Solving partial differential equations (PDEs) efficiently is essential for analyzing complex physical systems. Recent advancements in leveraging deep learning for solving PDE have shown significant promise. However, machine learning methods, such as Physics-Informed Neural Networks (PINN), face challenges in handling high-order derivatives of neural network-parameterized functions. Inspired by Forward Laplacian, a recent method of accelerating Laplacian computation, we propose an efficient computational framework, Differential Operator with Forward-propagation (DOF), for calculating general second-order differential operators without losing any precision. We provide rigorous proof of the advantages of our method over existing methods, demonstrating two times improvement in efficiency and reduced memory consumption on any architectures. Empirical results illustrate that our method surpasses traditional automatic differentiation (AutoDiff) techniques, achieving 2x improvement on the MLP structure and nearly 20x improvement on the MLP with Jacobian sparsity.

cs.LG↗

arXiv2023

Sleep When Everything Looks Fine: Self-Triggered Monitoring for Signal Temporal Logic Tasks

Online monitoring is a widely used technique in assessing if the performance of the system satisfies some desired requirements during run-time operation. Existing works on online monitoring usually assume that the monitor can acquire system information periodically at each time instant. However, such a periodic mechanism may be unnecessarily energy-consuming as it essentially requires to turn on sensors consistently. In this paper, we proposed a novel self-triggered mechanism for model-based online monitoring of discrete-time dynamical system under specifications described by signal temporal logic (STL) formulae. Specifically, instead of sampling the system state at each time instant, a self-triggered monitor can actively determine when the next system state is sampled in addition to its monitoring decision regarding the satisfaction of the task. We propose an effective algorithm for synthesizing such a self-triggered monitor that can correctly evaluate a given STL formula on-the-fly while maximizing the time interval between two observations. We show that, compared with the standard online monitor with periodic information, the proposed self-triggered monitor can significantly reduce observation burden while ensuring that no information of the STL formula is lost. Case studies are provided to illustrate the proposed monitoring mechanism.

eess.SY↗

arXiv2023

Forward Laplacian: A New Computational Framework for Neural Network-based Variational Monte Carlo

Neural network-based variational Monte Carlo (NN-VMC) has emerged as a promising cutting-edge technique of ab initio quantum chemistry. However, the high computational cost of existing approaches hinders their applications in realistic chemistry problems. Here, we report the development of a new NN-VMC method that achieves a remarkable speed-up by more than one order of magnitude, thereby greatly extending the applicability of NN-VMC to larger systems. Our key design is a novel computational framework named Forward Laplacian, which computes the Laplacian associated with neural networks, the bottleneck of NN-VMC, through an efficient forward propagation process. We then demonstrate that Forward Laplacian is not only versatile but also facilitates more developments of acceleration methods across various aspects, including optimization for sparse derivative matrix and efficient neural network design. Empirically, our approach enables NN-VMC to investigate a broader range of atoms, molecules and chemical reactions for the first time, providing valuable references to other ab initio methods. The results demonstrate a great potential in applying deep learning methods to solve general quantum mechanical problems.

physics.comp-ph↗

arXiv2022

Is $L^2$ Physics-Informed Loss Always Suitable for Training Physics-Informed Neural Network?

The Physics-Informed Neural Network (PINN) approach is a new and promising way to solve partial differential equations using deep learning. The $L^2$ Physics-Informed Loss is the de-facto standard in training Physics-Informed Neural Networks. In this paper, we challenge this common practice by investigating the relationship between the loss function and the approximation quality of the learned solution. In particular, we leverage the concept of stability in the literature of partial differential equation to study the asymptotic behavior of the learned solution as the loss approaches zero. With this concept, we study an important class of high-dimensional non-linear PDEs in optimal control, the Hamilton-Jacobi-Bellman(HJB) Equation, and prove that for general $L^p$ Physics-Informed Loss, a wide class of HJB equation is stable only if $p$ is sufficiently large. Therefore, the commonly used $L^2$ loss is not suitable for training PINN on those equations, while $L^{\infty}$ loss is a better choice. Based on the theoretical insight, we develop a novel PINN training algorithm to minimize the $L^{\infty}$ loss for HJB equations which is in a similar spirit to adversarial training. The effectiveness of the proposed algorithm is empirically demonstrated through experiments. Our code is released at https://github.com/LithiumDA/L_inf-PINN.

cs.LG↗

arXiv2022

Model Predictive Control for Signal Temporal Logic Specifications with Time Interval Decomposition

In this paper, we investigate the problem of Model Predictive Control (MPC) of dynamic systems for high-level specifications described by Signal Temporal Logic (STL) formulae. Recent works show that MPC has the great potential in handling logical tasks in reactive environments. However, existing approaches suffer from the heavy computational burden, especially for tasks with large horizons. In this work, we propose a computationally more efficient MPC framework for STL tasks based on time interval decomposition. Specifically, we still use the standard shrink horizon MPC framework with Mixed Integer Linear Programming (MILP) techniques for open-loop optimization problems. However, instead of applying MPC directly for the entire task horizon, we decompose the STL formula into several sub-formulae with disjoint time horizons, and shrinking horizon MPC is applied for each short-horizon sub-formula iteratively. To guarantee the satisfaction of the entire STL formula and to ensure the recursive feasibility of the iterative process, we introduce new terminal constraints to connect each sub-formula. We show how these terminal constraints can be computed by an effective inner-approximation approach. The computational efficiency of our approach is illustrated by a case study.

eess.SY↗