arXiv Machine Learning By Volkan Da\u{g}l{\i}, Zerrin Da\u{g}l{\i}, Da\u{g}han Da\u{g}l{\i}

Orbital Error Dynamics: Self-Organized Criticality, Ephemeral Parameter Resonance, and Non-Linear Biological Ontologies in Zero-Storage Neural Synthesis

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The paper introduces Orbital Error Dynamics (OED), an analytical framework that reinterprets neural network weights as transient topological resonances rather than static matrices, derived from a complex quadratic polynomial map. It proposes the Bent Sine Wave Hypothesis to explain non‑equilibrium living systems, defines Observer Horizon Geometry in parameter space, and presents a heavy‑tailed Biomimetic Perturbed Jump Operator inspired by biological processes. Empirical tests on the Two‑Moons manifold show that procedural parameterization from a 24‑byte seed yields competitive accuracy compared to a conventional gradient baseline, while also aligning conceptually with an analog optical co‑processor.

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arXiv AI
Jul 20

Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation

arXiv:2607. 10439v2 Announce Type: replace-cross Abstract: We model human motor cortex, recorded during rest and motor-imagery BCI conditions, as a port-Hamiltonian system: a conservative interconnection (skew-symmetric coupling between band-limited neural phasors) together with a dissipative port whose state-dependent decay is set by a graph-neural-network surrogate.

By Dibakar Sigdel
arXiv AI
Aug 10

A Physics-Inspired Classical Digital Twin of Cortical Dynamics: A Band-Stratified Metriplectic Port-Hamiltonian Neural Network Learned from Brain-Computer-Interface EEG

arXiv:2607. 10439v3 Announce Type: replace-cross Abstract: We present a physics-inspired classical digital twin of brain-computer- interface (BCI) data: a graph neural network constrained to a band-stratified, metriplectic port-Hamiltonian form, with parameters learned from scalp EEG recorded during rest and motor imagery.

By Dibakar Sigdel
arXiv Machine Learning
Sep 25

Beyond Compression: Training Latent Representations for Stable Long-Horizon Rollout in Neural Surrogate Solvers

The paper investigates why latent neural surrogate solvers, which compress physical system dynamics into a lower‑dimensional space, often fail during long‑horizon autoregressive rollouts. It demonstrates that training the latent representation only for reconstruction leads to instability, and proposes a set of training interventions—Koopman operator learning, Hamming noise injection, and multi‑step rollout fine‑tuning—that align the latent space with long‑horizon forecasting. These interventions reduce long‑rollout error by about 40 % and achieve accuracy comparable to full‑resolution models while using far fewer floating‑point operations and GPU memory, enabling stable extrapolation in mesoscale crystal‑plasticity simulations of high‑cycle fatigue.

By Andreas E. Robertson, Ashley T. Lenau, John D. Shimanek, Benjamin A. Jasperson, Vivek Oommen, David L. Damm, Krishna Garikipati, Remi Dingreville