Fast dynamical similarity analysis

• URL: http://arxiv.org/abs/2511.22828v1
• Date: Fri, 28 Nov 2025 01:27:00 GMT
• Title: Fast dynamical similarity analysis
• Authors: Arman Behrad, Mitchell Ostrow, Mohammad Taha Fakharian, Ila Fiete, Christian Beste, Shervin Safavi,
• Abstract summary: Dynamical similarity methods offer a framework to compare the temporal structure of dynamical systems.<n>Here we introduce fast Dynamical Similarity Analysis (fastDSA), which is computationally far more efficient than previous methods.<n>We demonstrate that fastDSA is at least an order of magnitude faster than the previous methods.
• Score: 8.262399199942761
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: To understand how neural systems process information, it is often essential to compare one circuit with another, one brain with another, or data with a model. Traditional similarity measures ignore the dynamical processes underlying neural representations. Dynamical similarity methods offer a framework to compare the temporal structure of dynamical systems by embedding their (possibly) nonlinear dynamics into a globally linear space and there computing conjugacy metrics. However, identifying the best embedding and computing these metrics can be computationally slow. Here we introduce fast Dynamical Similarity Analysis (fastDSA), which is computationally far more efficient than previous methods while maintaining their accuracy and robustness. FastDSA introduces two key components that boost efficiency: (1) automatic selection of the effective model order of the Hankel (delay) embedding from the data via a data-driven singular-value threshold that identifies the informative subspace and discards noise to lower computational cost without sacrificing signal, and (2) a novel optimization procedure and objective, which replaces the slow exact orthogonality constraint in finding a minimal distance between dynamics matrices with a lightweight process to keep the search close to the space of orthogonal transformations. We demonstrate that fastDSA is at least an order of magnitude faster than the previous methods. Furthermore, we demonstrate that fastDSA has the properties of its ancestor, including its invariances and sensitivities to system dynamics. FastDSA, therefore, provides a computationally efficient and accurate method for dynamical similarity analysis.

Related papers

• Gradient Descent as a Perceptron Algorithm: Understanding Dynamics and Implicit Acceleration [67.12978375116599]
  We show that the steps of gradient descent (GD) reduce to those of generalized perceptron algorithms.<n>This helps explain the optimization dynamics and the implicit acceleration phenomenon observed in neural networks.
  arXiv  Detail & Related papers  (2025-12-12T14:16:35Z)
• Mixed Monotonicity Reachability Analysis of Neural ODE: A Trade-Off Between Tightness and Efficiency [1.7205106391379026]
  We propose a novel interval-based reachability method for neural ordinary differential equations (neural ODE)<n>We exploit the geometric structure of full initial sets and their boundaries via the homeomorphism property.<n>Our approach provides sound and computationally efficient over-approximations compared with CORA's zonotopes and NNV2.0 star set representations.
  arXiv  Detail & Related papers  (2025-10-15T10:25:32Z)
• Event-Aided Time-to-Collision Estimation for Autonomous Driving [28.13397992839372]
  We present a novel method that estimates the time to collision using a neuromorphic event-based camera. The proposed algorithm consists of a two-step approach for efficient and accurate geometric model fitting on event data. Experiments on both synthetic and real data demonstrate the effectiveness of the proposed method.
  arXiv  Detail & Related papers  (2024-07-10T02:37:36Z)
• A physics-informed neural network method for the approximation of slow invariant manifolds for the general class of stiff systems of ODEs [0.0]
  We present a physics-informed neural network (PINN) approach for the discovery of slow invariant manifold (SIMs) In contrast to other machine learning (ML) approaches that construct reduced order black box surrogate models, our approach, simultaneously decomposes the vector field into fast and slow components. We show that the proposed PINN scheme provides SIM approximations, of equivalent or even higher accuracy, than those provided by QSSA, PEA and CSP.
  arXiv  Detail & Related papers  (2024-03-18T09:10:39Z)
• A Multi-Grained Symmetric Differential Equation Model for Learning Protein-Ligand Binding Dynamics [73.35846234413611]
  In drug discovery, molecular dynamics (MD) simulation provides a powerful tool for predicting binding affinities, estimating transport properties, and exploring pocket sites. We propose NeuralMD, the first machine learning (ML) surrogate that can facilitate numerical MD and provide accurate simulations in protein-ligand binding dynamics. We demonstrate the efficiency and effectiveness of NeuralMD, achieving over 1K$times$ speedup compared to standard numerical MD simulations.
  arXiv  Detail & Related papers  (2024-01-26T09:35:17Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Benchmarking sparse system identification with low-dimensional chaos [1.5849413067450229]
  We systematically benchmark sparse regression variants by utilizing the dysts standardized database of chaotic systems. We demonstrate how this open-source tool can be used to quantitatively compare different methods of system identification. In all cases, we used ensembling to improve the noise robustness of SINDy and provide statistical comparisons.
  arXiv  Detail & Related papers  (2023-02-04T18:49:52Z)
• A Stable, Fast, and Fully Automatic Learning Algorithm for Predictive Coding Networks [65.34977803841007]
  Predictive coding networks are neuroscience-inspired models with roots in both Bayesian statistics and neuroscience. We show how by simply changing the temporal scheduling of the update rule for the synaptic weights leads to an algorithm that is much more efficient and stable than the original one.
  arXiv  Detail & Related papers  (2022-11-16T00:11:04Z)
• Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions [0.0]
  This work presents a data-driven, non-intrusive framework which combines ROM construction with reduced dynamics identification. The proposed approach leverages autoencoder neural networks with parametric sparse identification of nonlinear dynamics (SINDy) to construct a low-dimensional dynamical model. These aim at tracking the evolution of periodic steady-state responses as functions of system parameters, avoiding the computation of the transient phase, and allowing to detect instabilities and bifurcations.
  arXiv  Detail & Related papers  (2022-11-13T01:57:18Z)
• Distributed Dynamic Safe Screening Algorithms for Sparse Regularization [73.85961005970222]
  We propose a new distributed dynamic safe screening (DDSS) method for sparsity regularized models and apply it on shared-memory and distributed-memory architecture respectively. We prove that the proposed method achieves the linear convergence rate with lower overall complexity and can eliminate almost all the inactive features in a finite number of iterations almost surely.
  arXiv  Detail & Related papers  (2022-04-23T02:45:55Z)
• A Priori Denoising Strategies for Sparse Identification of Nonlinear Dynamical Systems: A Comparative Study [68.8204255655161]
  We investigate and compare the performance of several local and global smoothing techniques to a priori denoise the state measurements. We show that, in general, global methods, which use the entire measurement data set, outperform local methods, which employ a neighboring data subset around a local point.
  arXiv  Detail & Related papers  (2022-01-29T23:31:25Z)
• Low-Rank Hankel Tensor Completion for Traffic Speed Estimation [7.346671461427793]
  We propose a purely data-driven and model-free solution to the traffic state estimation problem. By imposing a low-rank assumption on this tensor structure, we can approximate characterize both global patterns and the unknown complex local dynamics. We conduct numerical experiments on both synthetic simulation data and real-world high-resolution data, and our results demonstrate the effectiveness and superiority of the proposed model.
  arXiv  Detail & Related papers  (2021-05-21T00:08:06Z)
• DiffPD: Differentiable Projective Dynamics with Contact [65.88720481593118]
  We present DiffPD, an efficient differentiable soft-body simulator with implicit time integration. We evaluate the performance of DiffPD and observe a speedup of 4-19 times compared to the standard Newton's method in various applications.
  arXiv  Detail & Related papers  (2021-01-15T00:13:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.