Radiative Transfer

Particle transport under multiple scattering is central to radiative transfer and plasma physics, yet high-fidelity Monte Carlo (MC) simulations must trace prohibitively many particles. Learning-based surrogates can amortize this cost, but typically train on expensive, well-converged MC solutions. We propose the Particle Transport Neural Operator (PTNO), a neural operator that learns particle transport surrogates directly from noisy, low-cost MC labels. Such labels pose two challenges: (1) high variance, which destabilizes standard supervised learning, and (2) a high dynamic range (HDR) spanning many orders of magnitude. For the first, we learn the solution operator from noisy labels of many configurations, amortizing MC cost and generalizing to unseen configurations. Because MC labels are unbiased, we show that the squared loss on them shares its minimizer with the loss on converged solutions, and our budget-allocation study over training scenes $M$, MC samples per render $N$, and independent renders per scene $K$ shows that many noisy scenes beat fewer converged ones. For the second, a nonlinear transform such as the logarithm biases noisy supervision. Instead, PTNO keeps labels in physical space and enforces positivity with a softplus output layer that represents small values effectively. We further train with a pointwise relative $L_2$ loss (PRelL2), the stop-gradient relative loss of HDR denoising and neural rendering, which normalizes each residual by the stop-gradient prediction instead of the noisy label. We demonstrate PTNO on neutron transport in fusion reactors and radiative transfer in participating media. On the two neutronics tasks, PTNO is $10^4$-$10^5\times$ faster than converged MC on the same CPU and $10^3$-$10^5\times$ cheaper than MC at matched accuracy; on the two radiative-transfer tasks, MC at matched accuracy costs $0.8$-$11\times$ as much as PTNO.

Strong chromospheric absorption lines such as H$α$ 6562.8 A and Ca II 8542.1 A provide vital diagnostics of plasma dynamics and thermal structure in the solar chromosphere. Multilayer spectral inversion (MLSI) offers a physically interpretable framework for modeling these lines using a finite number of radiative-transfer layers, but conventional MLSI relies on pixel-by-pixel nonlinear least-squares fitting, making it computationally expensive for large imaging spectroscopic data sets. Here, we introduce a physics-informed neural-network (PINN) framework to accelerate MLSI while preserving its analytic radiative-transfer formulation. The network predicts MLSI parameters directly from observed line profiles and passes them through a differentiable MLSI forward model to synthesize spectra. Training follows a two-stage approach: an initial stage optimized solely via spectral reconstruction loss, followed by fine-tuning that combines spectral consistency with parameter-space supervision from conventional MLSI results on a single reference image. This strategy eliminates the need for large precomputed training sets while maintaining physical interpretability. Applied to Fast Imaging Solar Spectrograph (FISS) observations from the Goode Solar Telescope (GST) targeting both quiet-Sun and active-region regions, MLSI-PINN parameter maps reproduce the primary spatial structures of direct inversions, achieving an arithmetic mean pixel-wise Pearson correlation coefficient of 0.933 across all evaluated parameters. The reconstructed spectra closely match both observed profiles and conventional MLSI fits. Post-training, MLSI-PINN processes a raster in approximately 5-15 seconds compared to 3-5 minutes for conventional MLSI, delivering an inference speedup of about 12-60 times without substantial loss in reconstruction quality, enabling efficient MLSI analysis on large chromospheric data sets.

In radiation transfer simulations, an M1 method achieves substantial computational savings by replacing the full angular transport equation with a low-order moment system. Because this reduced system is not closed, a closure model is required to represent the unknown higher-order moments using lower-order moments. While machine learning (ML)-based closures can improve accuracy beyond classical analytic closures, unconstrained learned closures may produce non-real characteristic speeds and consequently cause numerical solver breakdown. To guarantee real eigenvalues of the Jacobian associated with ML closures, we propose a hyperbolic neural closure for the M1 radiative transfer system. Rather than directly predicting closure terms, we parameterize the Jacobian through two neural networks: (i) a symmetric matrix network and (ii) a strictly convex entropy network whose Hessian defines a positive definite symmetrizer. These components are combined to yield a Jacobian that is similar to a symmetric matrix, thereby ensuring real eigenvalues. The closure is then reconstructed by numerical integration of the learned Jacobian field along a prescribed integration path. Numerical experiments show that the proposed closure not only achieves higher closure accuracy than classical analytic closures, but also improves solution accuracy and remains stable in discontinuous Galerkin simulations for radiative transfer problems.

Single-image dehazing aims to recover a clear scene from a hazy image and is generally formulated as an image-to-image translation task; however, it faces two limitations. Its performance depends heavily on the haze-formation priors embedded in the model. Prevailing methods adopt the Atmospheric Scattering Model (ASM), whose assumptions of single scattering and homogeneous media are often violated, leading to residual haze and color drift. Moreover, large-scale real hazy/clear pairs are impractical to collect, and existing synthesis approaches fail to reproduce the full complexity of natural haze. To address these issues, we present RTE-FM-Dehazer, a novel dehazing approach, together with a scalable data pipeline. Unlike the ASM, the Radiative Transfer Equation (RTE) jointly accounts for both scattering and absorption, naturally accommodating the non-homogeneous, multiple-scattering media that characterize real hazy scenes. Motivated by the structural similarity between the RTE diffusion-absorption term and the ODE in flow matching, we introduce a diffusion-absorption regularizer derived from a reduced RTE, to steer the flow matching trajectory at each step. Next, leveraging modern vision-language models, we build an automated pipeline and release P-HAZE, a dataset of 50000 realistic hazy/clear pairs. Extensive evaluations demonstrate that RTE-FM-Dehazer, trained solely on P-HAZE, effectively eliminates artifacts like residual haze and color drift, exhibits strong cross-domain generalization, and achieves leading results on five real-world dehazing benchmarks.

Thermal-infrared (TIR) hyperspectral imagery (HSI) provides critical scene information for various applications. However, its practical utility is severely limited by unique sensor degradations beyond the capabilities of existing restoration methods, which are ignorant of underlying thermal physics. Here, we propose HAIR (HADAR-based Image Restoration) as a physics-driven framework for ground-based TIR-HSI restoration. HAIR utilizes the HADAR rendering equation (HRE) and combines it with the atmospheric downwelling radiative transfer equation (RTE) to model TIR-HSI using temperature, emissivity, and texture (TeX) physical triplets. This physical model leads to a TeX decompose-synthesize strategy that guarantees physical consistency and spatio-spectral noise resilience, in stark contrast to existing approaches. Moreover, our framework uses a forward-modeled atmospheric downwelling reference, along with spectral smoothness of emissivity and blackbody radiation, to enable spectral calibration and generation that would otherwise be elusive. Our extensive experiments on the outdoor DARPA Invisible Headlights dataset and in-lab FTIR measurements show that HAIR consistently outperforms state-of-the-art methods across denoising, inpainting, spectral calibration, and spectral super-resolution, establishing a benchmark in objective accuracy and visual quality.

Atmospheric correction is a critical preprocessing step in optical remote sensing, but repeated high-fidelity radiative transfer simulations remain computationally expensive for dense look-up-table generation, sensitivity analysis, retrieval support, and operational preprocessing. This study presents a physics-aware multi-fidelity surrogate framework for emulating atmospheric correction coefficients using paired 6S and libRadtran simulations. Atmospheric and geometric states are sampled using Latin Hypercube Sampling, and both radiative transfer models are evaluated under matched conditions for Sentinel-2 bands using spectral-response-function-aware coefficient generation. The high-fidelity targets are path reflectance, total transmittance, and spherical albedo. A physics-guided Kolmogorov-Arnold Network, termed pKANrtm, receives the atmospheric state and low-fidelity 6S coefficients, predicts the residual relative to libRadtran, and reconstructs the high-fidelity coefficients. The pKANrtm model uses an Efficient-KAN architecture and is trained with a physics-consistency penalty applied in the original coefficient space. The proposed model is evaluated against state-of-the-art regression-based RTM surrogates. Across both standard and out-of-distribution evaluation settings, pKANrtm achieves the strongest overall predictive performance among the compared models. Runtime benchmarking demonstrates substantial acceleration relative to libRadtran, with GPU inference providing approximately four orders of magnitude single-sample speedup and batched inference reaching tens of thousands of samples per second. These results indicate that physics-aware multi-fidelity pKANrtm emulation provides an accurate, physically structured, and computationally efficient strategy for atmospheric correction coefficient generation.

This is our fourth work in the series on machine learning (ML) moment closure models for the radiative transfer equation (RTE). In the first three papers of this series, we considered the RTE in slab geometry in 1D1V (i.e. one dimension in physical space and one dimension in angular space), and introduced a gradient-based ML moment closure [1], then enforced the hyperbolicity through a symmetrizer [2], or together with physical characteristic speeds by learning the eigenvalues of the Jacobian matrix [3]. Here, we extend our framework to the RTE in 2D2V (i.e. two dimensions in physical space and two dimensions in angular space). The main idea is to preserve the leading part of the classical $P_N$ model and modify only the highest-order block row. By analyzing the structural properties of the $P_N$ model, we show that its coefficient matrices are symmetric and admit a block-tridiagonal structure. Then we use this property to introduce a block-diagonal symmetrizer for the ML moment model and derive explicit algebraic conditions on the closure blocks which guarantee the symmetrizable hyperbolicity of the resulting ML system. These conditions lead to a natural parametrization of the closure in terms of a symmetric positive definite matrix together with symmetric closure blocks, which can be learned from data while automatically enforcing symmetrizable hyperbolicity by construction. The numerical results show that the proposed framework improves upon the classical $P_N$ model while maintaining hyperbolicity.

Computational fluid dynamics (CFD) has become an essential tool for predicting fire behavior, yet maintaining both efficiency and accuracy remains challenging. A major source of computational cost in fire simulations is the modeling of radiation transfer, which is usually the dominant heat transfer mechanism in fires. Solving the high-dimensional radiative transfer equation (RTE) with traditional numerical methods can be a performance bottleneck. Here, we present a machine learning framework based on Fourier-enhanced multiple-input neural operators (Fourier-MIONet) as an efficient alternative to direct numerical integration of the RTE. We first investigate the performance of neural operator architectures for a small-scale 2D pool fire and find that Fourier-MIONet provides the most accurate radiative solution predictions. The approach is then extended to 3D CFD fire simulations, where the computational mesh is locally refined across multiple levels. In these high-resolution settings, monolithic surrogate models for direct field-to-field mapping become difficult to train and computationally inefficient. To address this issue, a nested Fourier-MIONet is proposed to predict radiation solutions across multiple mesh-refinement levels. We validate the approach on 3D McCaffrey pool fires simulated with FireFOAM, including fixed fire sizes and a unified model trained over a continuous range of heat release rates (HRRs). The proposed method achieves global relative errors of 2-4% for 3D varying-HRR scenarios while providing faster inference than the estimated cost of one finite-volume radiation solve in FireFOAM for the 16-solid-angle case. With fast and accurate inference, the surrogate makes higher-fidelity radiation treatments practical and enables the incorporation of more spectrally resolved radiation models into CFD fire simulations for engineering applications.

In scientific and engineering domains, modeling high-dimensional complex systems governed by partial differential equations (PDEs) remains challenging in terms of physical consistency and numerical stability. However, existing approaches, such as physics-informed neural networks (PINNs), typically rely on known physical fields or coefficients and enforce physical constraints via external loss functions, which can lead to training instability and make it difficult to handle high-dimensional or unobservable scenarios. To this end, we propose PhysFormer, a generative modeling framework that is self-consistent at both the data and physical levels. PhysFormer leverages a low-dimensional, physically interpretable latent space to learn key physical quantities directly from data without requiring known high-dimensional physical field parameters, and embeds the physical process of radiative flux generation within the network to ensure the physical consistency of the generated spectra. In high-dimensional, degenerate inversion tasks, PhysFormer constrains generation within physical limits and enhances spectral fidelity and inversion stability under varying signal-to-noise ratios (SNRs). More broadly, this approach shifts the physical processes from external loss functions into the generative mechanism itself, providing a physically consistent generative modeling paradigm for complex systems involving unknown or unobservable physical quantities.

Passive long-wave infrared (LWIR) absorption-based ranging relies on atmospheric absorption to estimate distances to objects from their emitted thermal radiation. First demonstrated decades ago for objects much hotter than the air and recently extended to scenes with low temperature variations, this ranging has depended on reflected radiance being negligible. Downwelling radiance is especially problematic, sometimes causing large inaccuracies. In two new ranging methods, we use characteristic features from ozone absorption to estimate the contribution of reflected downwelling radiance. The quadspectral method gives a simple closed-form range estimate from four narrowband measurements, two at a water vapor absorption line and two at an ozone absorption line. The hyperspectral method uses a broader spectral range to improve accuracy while also providing estimates of temperature, emissivity profiles, and contributions of downwelling from a collection of zenith angles. Experimental results demonstrate improved ranging accuracy, in one case reducing error from over 100 m when reflected light is not modeled to 6.8 m with the quadspectral method and 1.2 m with the hyperspectral method.