mlsanityData to 14 Oct 2026

BLADE: Bayesian Langevin Active Discovery with Replica Exchange for Identification of Complex Systems

arXiv 2503.02983 ↗First posted 4 Mar 2025stat.ML cs.LGcited by 0

Not on the map. Why?

Abstract (arXiv)

Traditional methods for system discovery frequently struggle with efficient data usage and uncertainty quantification. Identifying the governing equations of complex dynamical systems from data presents a significant challenge in scientific discovery, especially when high-quality measurements are scarce and expensive to obtain. To overcome these limitations, we propose Bayesian Langevin Active Discovery with Replica Exchange for Identification of Complex Systems (BLADE), a novel Bayesian framework that combines replica-exchange stochastic gradient Langevin Monte Carlo with active learning. By balancing gradient-driven exploration and exploitation in coefficient space, BLADE provides probabilistic parameter estimation and principled uncertainty quantification. Faced with data scarcity, the probabilistic foundation of BLADE further facilitates the integration of active learning through a hybrid acquisition strategy that combines predictive uncertainty with space-filling design, enabling efficient selection of informative samples. Across benchmark systems, BLADE reduces measurement requirements by roughly 60% for Lotka-Volterra and 40% for Burgers' equation relative to random sampling, demonstrating substantial data-efficiency gains. These results highlight BLADE as a general uncertainty-aware framework for discovering interpretable dynamical systems, particularly valuable when high-fidelity data acquisition is prohibitively expensive.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 29 of its 55 references that are in the map. First posted on arXiv 4 Mar 2025.

Builds on

29 of 55 references.

References · 29

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2017Solving high-dimensional partial differential equations using deep learningcited by 556
  3. 2019Cyclical Stochastic Gradient MCMC for Bayesian Deep Learningcited by 203
  4. 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 197
  5. 2020Weak SINDy For Partial Differential Equationscited by 155
  6. 2021Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and controlcited by 137
  7. 2017Underdamped Langevin MCMC: A non-asymptotic analysiscited by 133
  8. 2020SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamicscited by 125
  9. 2018Log-concave sampling: Metropolis-Hastings algorithms are fastcited by 118
  10. 2018Data Driven Governing Equations Approximation Using Deep Neural Networkscited by 96
  11. 2018Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systemscited by 89
  12. 2020Optimal dimension dependence of the Metropolis-Adjusted Langevin Algorithmcited by 57
17 more
  1. 2018Learning unknown ODE models with Gaussian processescited by 54
  2. 2018On the Convergence of the SINDy Algorithmcited by 49
  3. 2019Data-Driven Deep Learning of Partial Differential Equations in Modal Spacecited by 46
  4. 2017Sparsity information and regularization in the horseshoe and other shrinkage priorscited by 43
  5. 2020Non-convex Learning via Replica Exchange Stochastic Gradient MCMCcited by 34
  6. 2022Discovering and forecasting extreme events via active learning in neural operatorscited by 32
  7. 2022Bayesian Active Learning with Fully Bayesian Gaussian Processescited by 26
  8. 2021Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Spacecited by 25
  9. 2020Approximation error analysis of some deep backward schemes for nonlinear PDEscited by 21
  10. 2020Accelerating Nonconvex Learning via Replica Exchange Langevin Diffusioncited by 16
  11. 2024Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy datacited by 15
  12. 2019Gaussian Process Assisted Active Learning of Physical Lawscited by 14
  13. 2022Noise-aware Physics-informed Machine Learning for Robust PDE Discoverycited by 14
  14. 2023HyperSINDy: Deep Generative Modeling of Nonlinear Stochastic Governing Equationscited by 8
  15. 2021Learning Dynamics from Noisy Measurements using Deep Learning with a Runge-Kutta Constraintcited by 7
  16. 2024Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamicscited by 7
  17. 2024Inferring the Langevin Equation with Uncertainty via Bayesian Neural Networkscited by 4

Built on by

Not cited yet.