arXiv subjects

Dimitris Drikakis

Publications and source records attributed to Dimitris Drikakis.

3 recordsLinked to original sources

arXiv2026

Initial-Trace Insufficiency and Entropy-Accounting Separation in Finite-Volume Coarse Graining

Coarse finite-volume information does not automatically define an exact pathwise closure for the restricted evolution of a fine-grid realization. We study two one-step information boundaries that are distinct from recursive predictive memory. First, we show that parent averages together with complete initial parent-interface trace pairs are sufficient for one forward-Euler finite-volume transition with a deterministic two-state numerical flux, but they do not generally determine a completed second-order strong-stability-preserving Runge-Kutta, equivalently Heun, transition. An explicit scalar upwind collision shows that hidden interior data can affect later stage traces and hence the completed parent update, even when initial traces and parent averages agree. Second, we show that exact conservative one-step closure is not the same as entropy-accounting closure. A parent entropy balance obtained from a cellwise numerical entropy balance contains a subcell Jensen gap, a realized entropy-flux difference, and residual dissipation. For a declared Burgers-Rusanov conservative flux and a declared Rusanov-type numerical entropy flux, we construct a sign-indexed finite family in which all branches have identical parent averages, identical conservative interface registers, and identical next parent averages, while the entropy-interface register distinguishes every branch. Under the uniform branch law, the conservative channel leaves nonzero deterministic squared-error floors for both the raw entropy register and its cyclic divergence. The results give a concise finite-volume information-sufficiency test for multistage interface data and entropy-side accounting.

math.NA↗

arXiv2026

Exact Finite-Horizon Memory, Conditioning, and Dissipative Decay in Coarse Upwind Finite-Volume Prediction

Coarse finite-volume averages do not generally form a predictive state: realized interface fluxes close a conservative update, but distinct fine-grid states with identical parent averages can generate different future coarse histories. We analyze this failure for periodic scalar advection discretized by a first-order upwind finite-volume method with forward Euler time integration. We derive a finite-horizon observation-rank law: each additional observation exposes one new child-cell layer and contributes one fewer independent direction than the number of parent cells, until the unresolved layers are exhausted. Centralized prediction therefore requires one fewer additional coordinate than the number of parent cells per exposed layer, whereas product-local prediction requires one coordinate per layer in each parent. An anchored flux-divergence queue attains the centralized bound, identifies the periodic flux gauge, and, at saturation, forms a minimal autonomous predictive state with the parent averages. We then distinguish exact observability from stable recoverability. The collar-to-queue map becomes rapidly ill-conditioned as the Courant number decreases, so algebraically visible delayed information may fall below a prescribed numerical tolerance. For Courant numbers strictly between zero and one, we prove contraction of the nonconstant component under bounded arithmetic perturbations, with separate control of mean drift, an explicit perturbation neighborhood, and a grid-dependent decay time. Numerical experiments illustrate the rank ladder, effective-rank loss, queue conditioning, step-function flattening, and delayed coarse separation followed by dissipative decay. The results provide a solvable benchmark for assessing state sufficiency in coarse, reduced, multiscale, and learned scientific models.

math.NA↗

arXiv2025

Evaluating Large Language Models in Code Generation: INFINITE Methodology for Defining the Inference Index

This study introduces a new methodology for an Inference Index (InI), called INFerence INdex In Testing model Effectiveness methodology (INFINITE), aiming to evaluate the performance of Large Language Models (LLMs) in code generation tasks. The InI index provides a comprehensive assessment focusing on three key components: efficiency, consistency, and accuracy. This approach encapsulates time-based efficiency, response quality, and the stability of model outputs, offering a thorough understanding of LLM performance beyond traditional accuracy metrics. We applied this methodology to compare OpenAI's GPT-4o (GPT), OpenAI-o1 pro (OAI1), and OpenAI-o3 mini-high (OAI3) in generating Python code for the Long-Short-Term-Memory (LSTM) model to forecast meteorological variables such as temperature, relative humidity and wind velocity. Our findings demonstrate that GPT outperforms OAI1 and performs comparably to OAI3 regarding accuracy and workflow efficiency. The study reveals that LLM-assisted code generation can produce results similar to expert-designed models with effective prompting and refinement. GPT's performance advantage highlights the benefits of widespread use and user feedback.

cs.SE↗