arXiv subjects

Qiyun Cheng

Publications and source records attributed to Qiyun Cheng.

5 recordsLinked to original sources

arXiv2026

Equation Recast for Canonical Operator Learning Across Parametric PDEs

Learning solution operators across broad parameter ranges can require substantial coverage of both input functions and physical parameters, particularly for purely data-driven parametric models. In addition, the resulting models may fail silently outside the training distribution. We introduce equation recast, which reformulates parametric operator learning as the learning of a single canonical operator. Parameter-induced operator variations are derived analytically from the governing equation and absorbed into effective sources, enabling zero-shot prediction across new parameter regimes. Across multi-parameter, nonlinear, and singular PDE settings, equation recast supports extrapolation, integrates sparse heterogeneous datasets in a shared canonical representation, and uses loss of convergence as an internal warning signal for failure of the recast iteration. In high-fidelity tokamak simulations for nuclear fusion, the framework unifies electron-temperature data across four device geometries through canonical-domain mapping within one jointly trained operator. Equation recast provides a route toward reusable neural PDE solvers combining equation-guided transfer, data efficiency, and monitorable inference.

cs.LG↗

arXiv2026

Surrogate Modeling for Neutron Transport: A Neural Operator Approach

This work introduces a neural operator based surrogate modeling framework for neutron transport computation. Two architectures, the Deep Operator Network (DeepONet) and the Fourier Neural Operator (FNO), were trained for fixed source problems to learn the mapping from anisotropic neutron sources, Q(x,{\mu}), to the corresponding angular fluxes, {\psi}(x,{\mu}), in a one-dimensional slab geometry. Three distinct models were trained for each neural operator, corresponding to different scattering ratios (c = 0.1, 0.5, & 1.0), providing insight into their performance across distinct transport regimes (absorption-dominated, moderate, and scattering-dominated). The models were subsequently evaluated on a wide range of previously unseen source configurations, demonstrating that FNO generally achieves higher predictive accuracy, while DeepONet offers greater computational efficiency. Both models offered significant speedups that become increasingly pronounced as the scattering ratio increases, requiring <0.3% of the runtime of a conventional S_N solver. The surrogate models were further incorporated into the S_N k-eigenvalue solver, replacing the computationally intensive transport sweep loop with a single forward pass. Across varying fission cross sections and spatial-angular grids, both neural operator solvers reproduced reference eigenvalues with deviations up to 135 pcm for DeepONet and 112 pcm for FNO, while reducing runtime to <0.1% of that of the S_N solver on relatively fine grids. These results demonstrate the strong potential of neural operator frameworks as accurate, efficient, and generalizable surrogates for neutron transport, paving the way for real-time digital twin applications and repeated evaluations, such as in design optimization.

physics.comp-ph↗

arXiv2025

MD-PNOP: Equation-Recast Neural Operators for Minimal-Data Extrapolation and PDE Solver Acceleration

The computational overhead of traditional numerical solvers for partial differential equations (PDEs) remains a critical bottleneck for large-scale parametric studies and design optimization. We introduce a Minimal-Data Parametric Neural Operator Preconditioning (MD-PNOP) framework, which establishes a new strategy for accelerating parametric PDE solvers while strictly preserving physical constraints. To address the extrapolation limitation of neural operators, parameter-induced operator difference is recast as additional source terms and incorporated into an iterative solution scheme using a pretrained neural operator. This equation-recast formulation enables systematic parameter extrapolation from a single training configuration to a broad range of unseen parameter settings without retraining. The neural operator predictions are then embedded into iterative PDE solvers as improved initial guesses, thereby reducing convergence iterations without sacrificing accuracy. Unlike purely data-driven approaches, MD-PNOP guarantees that the governing equations remain fully enforced, eliminating concerns regarding loss of physics or interpretability. The framework is architecture-agnostic and is demonstrated using both DeepONet and FNO for Boltzmann transport equation solvers in neutron transport applications. Numerical results demonstrate that neural operators trained on a single set of constant parameters successfully accelerate solutions with heterogeneous, sinusoidal, and discontinuous parameter distributions. Moreover, MD-PNOP consistently achieves approximately 50% reduction in computational time while maintaining full-order fidelity for fixed-source, single-group eigenvalue, and multigroup coupled eigenvalue problems.

cs.LG↗

arXiv2025

An Adaptive Real-Time Forecasting Framework for Cryogenic Fluid Management in Space Systems

Accurate real-time forecasting of cryogenic tank behavior is essential for the safe and efficient operation of propulsion and storage systems in future deep-space missions. While cryogenic fluid management (CFM) systems increasingly require autonomous capabilities, conventional simulation methods remain hindered by high computational cost, model imperfections, and sensitivity to unanticipated boundary condition changes. To address these limitations, this study proposes an Adaptive Real-Time Forecasting Framework for Cryogenic Propellant Management in Space Systems, featuring a lightweight, non-intrusive method named ARCTIC (Adaptive Real-time Cryogenic Tank Inference and Correction). ARCTIC integrates real-time sensor data with precomputed nodal simulations through a data-driven correction layer that dynamically refines forecast accuracy without modifying the underlying model. Two updating mechanisms, auto-calibration and observation and correction, enable continuous adaptation to evolving system states and transient disturbances. The method is first assessed through synthetic scenarios representing self-pressurization, sloshing, and periodic operations, then validated using experimental data from NASA's Multipurpose Hydrogen Test Bed and K-Site facilities. Results demonstrate that ARCTIC significantly improves forecast accuracy under model imperfections, data noise, and boundary fluctuations, offering a robust real-time forecasting capability to support autonomous CFM operations. The framework's compatibility with existing simulation tools and its low computational overhead make it especially suited for onboard implementation in space systems requiring predictive autonomy.

physics.flu-dyn↗

arXiv2024

A Data-Driven Based Concurrent Coupling Approach for Cryogenic Propellant Tank Long-term Pressure Control Predictions

The design and optimization of cryogenic propellant storage tanks for NASA's future space missions require fast and accurate predictions of long-term fluid behaviors. Computational fluid dynamics (CFD) techniques are high-fidelity but computationally prohibitive. Coarse mesh nodal techniques are fast but heavily rely on empirical correlations to capture prominent three-dimensional phenomena. A data-driven based concurrent coupling (DCC) approach has been developed to integrate CFD with nodal techniques for efficient and accurate analysis. This concurrent coupling scheme generates case-specific correlations on the fly through a short period of co-solving CFD and nodal simulations, followed by a long-period nodal simulation with CFD-corrected solutions. This paper presents the approach development, stability analysis, and efficiency demonstration, specifically for modeling two-phase cryogenic propellant tank self-pressurization and periodic mixing phenomena. Linear regression is employed to derive the data-driven correlations. The self-pressurization experiments of Multipurpose Hydrogen Test Bed experiments and K-Site tank are used to validate the approach. The DCC approach accurately predicts temperature stratifications while reducing computational time by as much as 70% compared to pure CFD simulations. Additionally, the DCC approach mitigates the risks of numerical instability and correlation loss inherent in current domain decomposition or overlapping-based coupling methods, making it a flexible and user-friendly approach for integrated CFD and nodal analysis of cryogenic tank behaviors.

physics.flu-dyn↗