arXiv Machine Learning
Jun 16
Learning Hybrid Biophysical Neuron Models with Neural ODEs
arXiv:2606. 16693v1 Announce Type: cross Abstract: Biophysical neuron models link measurements of neural activity to underlying cellular mechanisms.
Fast Surrogate Modeling of Excitable and Oscillatory FitzHugh-Nagumo Dynamics with Parametric Neural Operators
arXiv:2609. 04549v1 Announce Type: new Abstract: The FitzHugh-Nagumo (FHN) system serves as a simplified model of neuronal voltage dynamics, capturing the activator-inhibitor structure behind both isolated action potentials and the rhythmic spiking seen across the brain.
Related stories
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.
arXiv Machine Learning
Sep 4
Time Without Timesteps: Simulating Coupled Dynamical Systems via Self-Consistency
The paper introduces a new method for simulating coupled dynamical systems that bypasses traditional time‑stepping. Instead of marching through time, each subsystem is represented by a neural surrogate that maps an entire driving trajectory and initial condition to a full output trajectory. Coupling is achieved by enforcing self‑consistency across these trajectories, turning the simulation into a fixed‑point problem over complete trajectories. Experiments on van der Pol oscillators and Hodgkin‑Huxley neuron networks show that only 4–10 Newton iterations are needed, compared to 1500 steps for a conventional integrator, and that the gradient can be computed without time recursion using GMRES. The spectral radius of the surrogate’s Jacobian predicts convergence, and the implicit gradient remains accurate even when unrolled backpropagation diverges.
arXiv Machine Learning
Aug 12
DEFT: Data-Efficient Frequency-domain Top-k Sampling via Inverse Discrete Fourier Transform for Spatiotemporal Dynamical Systems Modeling
arXiv:2608. 11019v1 Announce Type: new Abstract: Modeling spatiotemporal dynamical systems governed by partial differential equations (PDEs) poses two major challenges: it either requires expensive physics-based simulators that entail iterative numerical solving at high computational cost, or it depends on abundant training data, yet purely data-driven models often generalize poorly to downstream dynamic operating conditions.
arXiv Machine Learning
Jun 3
Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations
arXiv:2606. 03936v1 Announce Type: new Abstract: Neural operator surrogates (NO) approximate PDE solutions orders of magnitude faster than numerical solvers, but suffer from spectral bias: high-frequency content is systematically attenuated, limiting reliability where fine-scale structure matters.
arXiv Machine Learning
Jun 19
Neural Architectures as Functional Priors in Physics-Informed Control Problems
arXiv:2606. 19368v1 Announce Type: cross Abstract: In this work we investigate the role of neural architectures as implicit functional priors in control problems governed by ordinary differential equations.
arXiv Machine Learning
Aug 14
Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations
arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).
arXiv Machine Learning
Sep 22
A discrete generative model of neuronal spiking activity on microelectrode arrays
The paper presents a discrete generative model for neuronal spiking activity recorded on microelectrode arrays. It uses a shared vocabulary of spatiotemporal motifs learned by a residual vector‑quantized autoencoder and predicts motif occurrence with a factorized masked transformer. Evaluated on 31 assays from human brain organoids and ex vivo hippocampal tissue, the model achieves superior reconstruction and generation performance compared to baselines and shows that motifs are largely reused across assays.
arXiv AI
4d ago
Transolver-$\sigma$: Joint Spectral-Physical Subspace Modeling for Neural PDE Solving
Transolver‑σ is a neural PDE solver that jointly models spectral and physical subspaces to improve accuracy in both one‑step and autoregressive rollouts. The method uses adaptive physical-state interactions, Slice‑Residual Physics‑Attention, and an axis‑factorized Fourier operator to enable information exchange between representations. Across five standard PDE benchmarks, Transolver‑σ reduces benchmark‑averaged relative error by 33.4% compared to the strongest baseline and shows strong performance on coupled multiphysics systems and real‑world fluid and combustion data.
arXiv Machine Learning
Jul 7
Diffusion learning reveals viable parameter manifolds and compensation geometry in biological dynamical systems
arXiv:2607. 03671v1 Announce Type: cross Abstract: Models of complex systems often have many parameters, yet are constrained by far fewer experimentally accessible observables: similar activity can emerge from coordinated parameter changes.
arXiv Machine Learning
Sep 25
Orbital Error Dynamics: Self-Organized Criticality, Ephemeral Parameter Resonance, and Non-Linear Biological Ontologies in Zero-Storage Neural Synthesis
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.
arXiv Machine Learning
Jul 17
Scalable Training of Continuous-Time Spiking Neural Networks with Differentiable Spike-Time Discretization
arXiv:2607. 14672v1 Announce Type: new Abstract: Continuous-time spiking neural networks (SNNs) provide an event-driven framework for temporal computation, computational neuroscience, and neuromorphic hardware.