arXiv subjects

Y. Sungtaek Ju

Publications and source records attributed to Y. Sungtaek Ju.

11 recordsLinked to original sources

arXiv2026

Full-Scattering-Matrix Deterministic Phonon Boltzmann Transport Simulation

Solutions to the phonon Boltzmann transport equation under the relaxation-time approximation (RTA) are fundamentally limited in that they do not account for the off-diagonal elements of the scattering matrix, which encode intermode energy redistribution. We find that the phonon in-scattering matrix is globally incompressible, requiring nearly its full rank for any useful Frobenius accuracy. The incompressibility worsens as the Brillouin zone is refined. We show that, despite this difficulty, one can develop a computationally efficient 3D BTE solver incorporating the complete scattering matrix by leveraging our two structural discoveries: the non-equilibrium phonon distribution inhabits a remarkably low-dimensional subspace of mode space regardless of how many phonon modes exist, and the leading singular modes of the scattering operator align selectively with this transport-active subspace. Consequently, truncation incurs negligible transport error even under large norm error. The phonon streaming operator's mode-diagonal character further motivates a hybrid architecture that exploits these two properties. When applied to nanoscale structures emulating a fin field-effect transistor, our BTE solver quantifies a geometry-independent multiplicative correction to the temperature rise predicted under RTA. Our theoretical work and resulting BTE solver help enable rigorous study of phonon transport and systematic design of devices and structures in the ballistic and quasi-ballistic phonon transport regime.

physics.comp-ph↗

arXiv2026

Intermittency-Driven Turbulence Cascade Memory Extends the Markov-Einstein Coherence Length Beyond the Canonical Estimate

Using direct numerical simulation of forced isotropic turbulence at $\text{Re}_λ\approx 1300$ and $\approx 433$, together with two independent Markov-by-construction null surrogates, we measure the Markov--Einstein coherence length of the turbulent energy cascade to be $Δr \approx 3.2$-$3.6$ in log-scale cascade coordinates, approximately three times the canonical estimate $Δr \approx 1$. Stratifying the gap-scan test by local dissipation intensity and by increment amplitude reveals that intermittent events carry $Δr \approx 3$-$4$, while at mid-inertial-range scales the quiescent cascade recovers $Δr \approx 1.0$-$1.4$, consistent with the canonical value. Near the dissipation range this pattern reverses: bulk dynamics carry more memory than extreme events, consistent with the spectral bottleneck. The excess memory is internal to the inertial range and Reynolds-number-independent over $\text{Re}_λ\approx 433$-$1300$. These findings indicate that the Markov approximation underlying the cascade Fokker-Planck equation and fluctuation-theorem analyses is substantially more restrictive than previously assumed, and that a non-Markovian correction, informed by the amplitude-dependent memory structure identified here, is needed for the intermittent component of the cascade.

physics.flu-dyn↗

arXiv2026

SymCircuit: Bayesian Structure Inference for Tractable Probabilistic Circuits via Entropy-Regularized Reinforcement Learning

Probabilistic circuit (PC) structure learning is hampered by greedy algorithms that make irreversible, locally optimal decisions. We propose SymCircuit, which replaces greedy search with a learned generative policy trained via entropy-regularized reinforcement learning. Instantiating the RL-as-inference framework in the PC domain, we show the optimal policy is a tempered Bayesian posterior, recovering the exact posterior when the regularization temperature is set inversely proportional to the dataset size. The policy is implemented as SymFormer, a grammar-constrained autoregressive Transformer with tree-relative self-attention that guarantees valid circuits at every generation step. We introduce option-level REINFORCE, restricting gradient updates to structural decisions rather than all tokens, yielding an SNR (signal to noise ratio) improvement and >10 times sample efficiency gain on the NLTCS dataset. A three-layer uncertainty decomposition (structural via model averaging, parametric via the delta method, leaf via conjugate Dirichlet-Categorical propagation) is grounded in the multilinear polynomial structure of PC outputs. On NLTCS, SymCircuit closes 93% of the gap to LearnSPN; preliminary results on Plants (69 variables) suggest scalability.

cs.LG↗

arXiv2026

Spectral Homogenization of the Radiative Transfer Equation via Low-Rank Tensor Train Decomposition

Radiative transfer in absorbing-scattering media requires solving a transport equation across a spectral domain with 10^5 - 10^6 molecular absorption lines. Line-by-line (LBL) computation is prohibitively expensive, while existing approximations sacrifice spectral fidelity. We show that the Young-measure homogenization framework produces solution tensors I that admit low-rank tensor-train (TT) decompositions whose bond dimensions remain bounded as the spectral resolution Ns increases. Using molecular line parameters from the HITRAN database for H2O and CO2, we demonstrate that: (i) the TT rank saturates at r = 8 (at tolerance e = 10^-6) from Ns = 16 to 4096, independent of single-scattering albedo, Henyey-Greenstein asymmetry, temperature, and pressure; (ii) quantized tensor-train (QTT) representations achieve sub-linear storage scaling; (iii) in a controlled comparison using identical opacity data and transport solver, the homogenized approach achieves over an order of magnitude lower L2 error than the correlated-k distribution at equal cost; and (iv) for atomic plasma opacity (aluminum at 60 eV, TOPS database), the TT rank saturates at r = 15 with fundamentally different spectral structure (bound-bound and bound-free transitions spanning 12 decades of dynamic range), confirming that rank boundedness is a property of the transport equation rather than any particular opacity source. These results establish that the spectral complexity of radiative transfer has a finite effective rank exploitable by tensor decomposition, complementing the spatial-angular compression achieved by existing TT and dynamical low-rank approaches.

physics.chem-ph↗

arXiv2026

SymPlex: A Structure-Aware Transformer for Symbolic PDE Solving

We propose SymPlex, a reinforcement learning framework for discovering analytical symbolic solutions to partial differential equations (PDEs) without access to ground-truth expressions. SymPlex formulates symbolic PDE solving as tree-structured decision-making and optimizes candidate solutions using only the PDE and its boundary conditions. At its core is SymFormer, a structure-aware Transformer that models hierarchical symbolic dependencies via tree-relative self-attention and enforces syntactic validity through grammar-constrained autoregressive decoding, overcoming the limited expressivity of sequence-based generators. Unlike numerical and neural approaches that approximate solutions in discretized or implicit function spaces, SymPlex operates directly in symbolic expression space, enabling interpretable and human-readable solutions that naturally represent non-smooth behavior and explicit parametric dependence. Empirical results demonstrate exact recovery of non-smooth and parametric PDE solutions using deep learning-based symbolic methods.

cs.LG↗

arXiv2025

Uncertainty-Aware Flow Field Reconstruction Using SVGP Kolmogorov-Arnold Networks

Reconstructing time-resolved flow fields from temporally sparse velocimetry measurements is critical for characterizing many complex thermal-fluid systems. We introduce a machine learning framework for uncertainty-aware flow reconstruction using sparse variational Gaussian processes in the Kolmogorov-Arnold network topology (SVGP-KAN). This approach extends the classical foundations of Linear Stochastic Estimation (LSE) and Spectral Analysis Modal Methods (SAMM) while enabling principled epistemic uncertainty quantification. We perform a systematic comparison of our framework with the classical reconstruction methods as well as Kalman filtering. Using synthetic data from pulsed impingement jet flows, we assess performance across fractional PIV sampling rates ranging from 0.5% to 10%. Evaluation metrics include reconstruction error, generalization gap, structure preservation, and uncertainty calibration. Our SVGP-KAN methods achieve reconstruction accuracy comparable to established methods, while also providing well-calibrated uncertainty estimates that reliably indicate when and where predictions degrade. The results demonstrate a robust, data-driven framework for flow field reconstruction with meaningful uncertainty quantification and offer practical guidance for experimental design in periodic flows.

physics.flu-dyn↗

arXiv2025

Uncertainty Quantification for Scientific Machine Learning using Sparse Variational Gaussian Process Kolmogorov-Arnold Networks (SVGP KAN)

Kolmogorov-Arnold Networks have emerged as interpretable alternatives to traditional multi-layer perceptrons. However, standard implementations lack principled uncertainty quantification capabilities essential for many scientific applications. We present a framework integrating sparse variational Gaussian process inference with the Kolmogorov-Arnold topology, enabling scalable Bayesian inference with computational complexity quasi-linear in sample size. Through analytic moment matching, we propagate uncertainty through deep additive structures while maintaining interpretability. We use three example studies to demonstrate the framework's ability to distinguish aleatoric from epistemic uncertainty: calibration of heteroscedastic measurement noise in fluid flow reconstruction, quantification of prediction confidence degradation in multi-step forecasting of advection-diffusion dynamics, and out-of-distribution detection in convolutional autoencoders. These results suggest Sparse Variational Gaussian Process Kolmogorov-Arnold Networks (SVGP KANs) is a promising architecture for uncertainty-aware learning in scientific machine learning.

cs.LG↗

arXiv2025

Scalable and Interpretable Scientific Discovery via Sparse Variational Gaussian Process Kolmogorov-Arnold Networks (SVGP KAN)

Kolmogorov-Arnold Networks (KANs) offer a promising alternative to Multi-Layer Perceptron (MLP) by placing learnable univariate functions on network edges, enhancing interpretability. However, standard KANs lack probabilistic outputs, limiting their utility in applications requiring uncertainty quantification. While recent Gaussian Process (GP) extensions to KANs address this, they utilize exact inference methods that scale cubically with data size N, restricting their application to smaller datasets. We introduce the Sparse Variational GP-KAN (SVGP-KAN), an architecture that integrates sparse variational inference with the KAN topology. By employing $M$ inducing points and analytic moment matching, our method reduces computational complexity from $O(N^3)$ to $O(NM^2)$ or linear in sample size, enabling the application of probabilistic KANs to larger scientific datasets. Furthermore, we demonstrate that integrating a permutation-based importance analysis enables the network to function as a framework for structural identification, identifying relevant inputs and classifying functional relationships.

cs.LG↗

arXiv2025

Dynamics of thin film flows on a vertical fibre with vapor absorption

Water vapor capture through free surface flows plays a crucial role in various industrial applications, such as liquid desiccant air conditioning systems, water harvesting, and dewatering. This paper studies the dynamics of a silicone liquid sorbent (also known as water-absorbing silicone oil) flowing down a vertical cylindrical fibre while absorbing water vapor. We propose a one-sided thin-film-type model for these dynamics, where the governing equations form a coupled system of nonlinear fourth-order partial differential equations for the liquid film thickness and oil concentration. The model incorporates gravity, surface tension, Marangoni effects induced by concentration gradients, and non-mass-conserving effects due to absorption flux. Interfacial instabilities, driven by the competition between mass-conserving and non-mass-conserving effects, are investigated via stability analysis. We numerically show that water absorption can lead to the formation of irregular wavy patterns and trigger droplet coalescence downstream. Systematic simulations further identify parameter ranges for the Marangoni number and absorption parameter that lead to the onset of droplet coalescence dynamics and regime transitions.

physics.flu-dyn↗

arXiv2023

A positivity-preserving numerical method for a thin liquid film on a vertical cylindrical fiber

When a thin liquid film flows down on a vertical fiber, one can observe the complex and captivating interfacial dynamics of an unsteady flow. Such dynamics are applicable in various fluid experiments due to their high surface area-to-volume ratio. Recent studies verified that when the flow undergoes regime transitions, the magnitude of the film thickness changes dramatically, making numerical simulations challenging. In this paper, we present a computationally efficient numerical method that can maintain the positivity of the film thickness as well as conserve the volume of the fluid under the coarse mesh setting. A series of comparisons to laboratory experiments and previously proposed numerical methods supports the validity of our numerical method. We also prove that our method is second-order consistent in space and satisfies the entropy estimate.

math.NA↗

arXiv2020

Modeling film flows down a fibre influenced by nozzle geometry

We study the effects of nozzle geometry on the dynamics of thin fluid films flowing down a vertical cylindrical fibre. Recent experiments show that varying the nozzle diameter can lead to different flow regimes and droplet characteristics in the film. Using a weighted residual modeling approach, we develop a system of coupled equations that account for inertia, surface tension effects, gravity, and a film stabilization mechanism to describe both near-nozzle fluid structures and downstream bead dynamics. We report good agreement between the predicted droplet properties and the experimental data.

physics.flu-dyn↗