arXiv subjects

Brandon Yee

Publications and source records attributed to Brandon Yee.

8 recordsLinked to original sources

arXiv2026

When Attention Beats Fourier: Multi-Scale Transformers for PDE Solving on Irregular Domains

We study the problem of \emph{architecture selection} for deep learning models trained to solve partial differential equations (PDEs), asking when transformer-based architectures with learned attention outperform Fourier-domain neural operators. We introduce the \textbf{Multi-Scale Attention Transformer} (\msat{}), a deep learning architecture that encodes spatiotemporal solution histories as token sequences and trains end-to-end via a composite supervised objective with optional physics-informed regularization terms. We conduct a comprehensive empirical evaluation against nine baselines -- including physics-informed neural networks (PINNs), neural operators (FNO, DeepONet, GNOT), and state-space models (Mamba-NO) -- across five benchmark problems from the PINNacle suite, using identical train/test splits and reference data for all methods. \msat{} achieves state-of-the-art generalization on complex geometry problems ($L^2_\mathrm{rel} = 0.0101$ on Heat2D-CG, a $3.7\times$ improvement over FNO) at $34\,\mathrm{s}$ total inference vs.\ $120{,}812\,\mathrm{s}$ for Mamba-NO. Ablation studies over the physics regularization component reveal a precise inductive bias tradeoff: physics priors reduce test error on diffusion-dominated problems but degrade generalization on chaotic and recirculating-flow regimes, directly characterizing the prior misspecification boundary. Approximation error bounds as a function of domain boundary complexity $\kappa$ provide a theoretical basis for these empirical findings and a principled rule for architecture selection.

cs.LG↗

arXiv2026

PI-JEPA: Label-Free Surrogate Pretraining for Coupled Multiphysics Simulation via Operator-Split Latent Prediction

Reservoir simulation workflows face a fundamental data asymmetry: input parameter fields (geostatistical permeability realizations, porosity distributions) are free to generate in arbitrary quantities, yet existing neural operator surrogates require large corpora of expensive labeled simulation trajectories and cannot exploit this unlabeled structure. We introduce \textbf{PI-JEPA} (Physics-Informed Joint Embedding Predictive Architecture), a surrogate pretraining framework that trains \emph{without any completed PDE solves}, using masked latent prediction on unlabeled parameter fields under per-sub-operator PDE residual regularization. The predictor bank is structurally aligned with the Lie--Trotter operator-splitting decomposition of the governing equations, dedicating a separate physics-constrained latent module to each sub-process (pressure, saturation transport, reaction), enabling fine-tuning with as few as 100 labeled simulation runs. On single-phase Darcy flow, PI-JEPA achieves $1.9\times$ lower error than FNO and $2.4\times$ lower error than DeepONet at $N_\ell{=}100$, with 24\% improvement over supervised-only training at $N_\ell{=}500$, demonstrating that label-free surrogate pretraining substantially reduces the simulation budget required for multiphysics surrogate deployment.

cs.LG↗

arXiv2026

Beam-Plasma Collective Oscillations in Intense Charged-Particle Beams: Dielectric Response Theory, Langmuir Wave Dispersion, and Unsupervised Detection via Prometheus

We develop a theoretical and computational framework for beam-plasma collective oscillations in intense charged-particle beams at intermediate energies (10-100 MeV). In Part I, we formulate a kinetic field theory governed by the Vlasov-Poisson system, deriving the Lindhard dielectric function and random phase approximation (RPA) polarization tensor for three beam distribution functions. We prove via the dielectric function epsilon(omega,q)=0 the existence of undamped Langmuir wave modes above a critical beam density n_c, obtain explicit beam-plasma dispersion relations, and show that Landau damping vanishes above the particle-hole continuum. The plasma frequency Omega_p^2 = ne^2/(m*epsilon_0) is fixed by the f-sum rule independently of distribution shape; higher dispersion coefficients depend on velocity moments. Space charge effects drive anomalous beam broadening with sqrt(n-n_c) onset and Friedel oscillations at q=2k_F. The beam-plasma transition belongs to the 3D Ising universality class via renormalization group analysis. In Part II, we validate these predictions using Prometheus, a beta-VAE trained on static structure factor data S(q) from particle-in-cell (PIC) beam simulations. Prometheus detects collective plasma oscillation onset in Gaussian and uniform distributions, confirms their absence in the degenerate Fermi gas (n_c -> 0), and resolves the Kohn anomaly at q=2k_F. Dispersion analysis of S(q,omega) from PIC simulations verifies the distribution-independent Omega_p predicted by the f-sum rule. All six validation checks pass. Predicted signatures -- density-tunable plasma resonances at omega_p proportional to sqrt(n), anomalous beam broadening with sqrt(n-n_c) onset, and Friedel oscillations -- are accessible at existing intermediate-energy beam facilities.

physics.plasm-ph↗

arXiv2026

Benchmarking Emergent Coordination in Large-Scale LLM Populations: An Evaluation Framework on the MoltBook Archive

As multi-agent Large Language Model (LLM) systems scale, evaluating their emergent coordination dynamics becomes increasingly critical. However, current evaluation paradigms-focused on single agents or small, explicitly structured groups-fail to capture the self-organization and viral information dynamics that arise in large, decentralized populations. We introduce a systematic evaluation framework to benchmark role specialization, information diffusion, and cooperative task resolution in open agent environments. We demonstrate this framework on the MoltBook Observatory Archive, a dataset of 2.73M interactions among 90,704 autonomous agents, establishing quantitative baselines for emergent coordination. Our evaluation reveals a pronounced core-periphery structure (silhouette 0.91), heavy-tailed cascade distributions ($\alpha = 2.57$), and severe coordination overhead in decentralized task resolution (Cohen's $d = -0.88$ against a single-agent baseline). By providing standardized evaluation tasks and empirical baselines, our framework enables the rigorous comparison of future multi-agent protocols and establishes evaluation itself as an object of scientific study.

cs.MA↗

arXiv2026

Geodesic Semantic Search: Cartographic Navigation of Citation Graphs with Learned Local Riemannian Maps

We present Geodesic Semantic Search (GSS), a retrieval system that learns node-specific Riemannian metrics on citation graphs to enable geometry-aware semantic search. Unlike standard embedding-based retrieval that relies on fixed Euclidean distances, \gss{} learns a low-rank metric tensor $\mL_i \in \R^{d \times r}$ at each node, inducing a local positive semi-definite metric $\mG_i = \mL_i \mL_i^\top + \eps \mI$. This parameterization guarantees valid metrics while keeping the model tractable. Retrieval proceeds via multi-source Dijkstra on the learned geodesic distances, followed by Maximal Marginal Relevance reranking and path coherence filtering. On citation prediction benchmarks with 169K arXiv papers, GSS achieves 23\% relative improvement in Recall@20 over SPECTER+FAISS baselines. We provide a Bridge Recovery Guarantee characterizing when geodesic retrieval qualitatively outperforms direct similarity, a margin separation result connecting training loss to retrieval quality, and characterize the expressiveness of low-rank metric parameterization. Our hierarchical coarse-to-fine search with k-means pooling reduces computational cost by $4\times$ while maintaining 97\% retrieval quality.

cs.IR↗

arXiv2026

Unsupervised Discovery of Intermediate Phase Order in the Frustrated $J_1$-$J_2$ Heisenberg Model via Prometheus Framework

The spin-$1/2$ $J_1$-$J_2$ Heisenberg model on the square lattice exhibits a debated intermediate phase between N\'eel antiferromagnetic and stripe ordered regimes, with competing theories proposing plaquette valence bond, nematic, and quantum spin liquid ground states. We apply the Prometheus variational autoencoder framework -- previously applied to classical (2D, 3D Ising) and quantum (disordered transverse field Ising) phase transitions -- to systematically explore the $J_1$-$J_2$ phase diagram using a multi-scale approach. For $L=4$, we employ exact diagonalization with full wavefunction analysis via quantum-aware VAE. For larger systems ($L=6, 8$), we introduce a reduced density matrix (RDM) based methodology using DMRG ground states, enabling scaling beyond the exponential barrier of full Hilbert space representation. Through dense parameter scans of $J_2/J_1 \in [0, 1]$ and comprehensive latent space analysis, we identify the structure factor $S(\pi,\pi)$ and $S(\pi,0)$ as the dominant order parameters discovered by the VAE, with correlations exceeding $|r| > 0.97$. The RDM-VAE approach successfully captures the N\'eel-to-stripe crossover near $J_2/J_1 \approx 0.5$--$0.6$, demonstrating that local quantum correlations encoded in reduced density matrices contain sufficient information for unsupervised phase discovery. This work establishes a scalable pathway for applying machine learning to frustrated quantum systems where full wavefunction access is computationally prohibitive.

cond-mat.str-el↗

arXiv2026

From Classical to Quantum: Extending Prometheus for Unsupervised Discovery of Phase Transitions in Three Dimensions and Quantum Systems

We extend the Prometheus framework for unsupervised phase transition discovery from two-dimensional classical systems to three-dimensional classical systems and quantum many-body systems. Building upon preliminary observations from a 2D Ising model student abstract [Yee et al., 2026], we address two fundamental questions: (1) Does the framework scale to higher dimensions where exact solutions are unavailable? (2) Can it generalize to quantum phase transitions driven by quantum fluctuations rather than thermal fluctuations? For the 3D Ising model on lattices up to $L{=}32$, we achieve critical temperature detection within 0.01\% of literature values ($\Tc/J = 4.511 \pm 0.005$) and extract critical exponents with ${\geq}70\%$ accuracy, with statistical analysis correctly identifying the 3D Ising universality class ($p = 0.72$). For quantum systems, we develop quantum-aware VAE (Q-VAE) architectures operating on complex-valued wavefunctions with fidelity-based loss functions, achieving 2\% accuracy in quantum critical point detection for the transverse field Ising model. For the disordered TFIM, we perform a consistency check of activated dynamical scaling $\ln \xi \sim |h - \hc|^{-\psi}$, extracting tunneling exponent $\psi = 0.48 \pm 0.08$ consistent with theoretical predictions ($\psi = 0.5$, $\Delta\chi^2 = 12.3$, $p < 0.001$). This demonstrates that unsupervised learning can identify qualitatively different \emph{types} of critical behavior, serving as a consistency check on known IRFP physics.

cond-mat.dis-nn↗

arXiv2026

Calibrating Behavioral Parameters with Large Language Models

Behavioral parameters such as loss aversion, herding, and extrapolation are central to asset pricing models but remain difficult to measure reliably. We develop a framework that treats large language models (LLMs) as calibrated measurement instruments for behavioral parameters. Using four models and 24{,}000 agent--scenario pairs, we document systematic rationality bias in baseline LLM behavior, including attenuated loss aversion, weak herding, and near-zero disposition effects relative to human benchmarks. Profile-based calibration induces large, stable, and theoretically coherent shifts in several parameters, with calibrated loss aversion, herding, extrapolation, and anchoring reaching or exceeding benchmark magnitudes. To assess external validity, we embed calibrated parameters in an agent-based asset pricing model, where calibrated extrapolation generates short-horizon momentum and long-horizon reversal patterns consistent with empirical evidence. Our results establish measurement ranges, calibration functions, and explicit boundaries for eight canonical behavioral biases.

econ.GN↗