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

arXiv: https://arxiv.org/abs/2503.02983 · HTML: https://mlsanity.com/paper/2503.02983/

## 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 (most cited first, 29 of 29)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1507.05021/) (2015)
- [Weak SINDy For Partial Differential Equations](https://mlsanity.com/paper/2007.02848/) (2020)
- [Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control](https://mlsanity.com/paper/2111.10992/) (2021)
- [Underdamped Langevin MCMC: A non-asymptotic analysis](https://mlsanity.com/paper/1707.03663/) (2017)
- [SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics](https://mlsanity.com/paper/2004.02322/) (2020)
- [Log-concave sampling: Metropolis-Hastings algorithms are fast](https://mlsanity.com/paper/1801.02309/) (2018)
- [Data Driven Governing Equations Approximation Using Deep Neural Networks](https://mlsanity.com/paper/1811.05537/) (2018)
- [Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1801.01236/) (2018)
- [Optimal dimension dependence of the Metropolis-Adjusted Langevin Algorithm](https://mlsanity.com/paper/2012.12810/) (2020)
- [Learning unknown ODE models with Gaussian processes](https://mlsanity.com/paper/1803.04303/) (2018)
- [On the Convergence of the SINDy Algorithm](https://mlsanity.com/paper/1805.06445/) (2018)
- [Data-Driven Deep Learning of Partial Differential Equations in Modal Space](https://mlsanity.com/paper/1910.06948/) (2019)
- [Sparsity information and regularization in the horseshoe and other shrinkage priors](https://mlsanity.com/paper/1707.01694/) (2017)
- [Non-convex Learning via Replica Exchange Stochastic Gradient MCMC](https://mlsanity.com/paper/2008.05367/) (2020)
- [Discovering and forecasting extreme events via active learning in neural operators](https://mlsanity.com/paper/2204.02488/) (2022)
- [Bayesian Active Learning with Fully Bayesian Gaussian Processes](https://mlsanity.com/paper/2205.10186/) (2022)
- [Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space](https://mlsanity.com/paper/2106.03603/) (2021)
- [Approximation error analysis of some deep backward schemes for nonlinear PDEs](https://mlsanity.com/paper/2006.01496/) (2020)
- [Accelerating Nonconvex Learning via Replica Exchange Langevin Diffusion](https://mlsanity.com/paper/2007.01990/) (2020)
- [Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy data](https://mlsanity.com/paper/2402.15357/) (2024)
- [Gaussian Process Assisted Active Learning of Physical Laws](https://mlsanity.com/paper/1910.03120/) (2019)
- [Noise-aware Physics-informed Machine Learning for Robust PDE Discovery](https://mlsanity.com/paper/2206.12901/) (2022)
- [HyperSINDy: Deep Generative Modeling of Nonlinear Stochastic Governing Equations](https://mlsanity.com/paper/2310.04832/) (2023)
- [Learning Dynamics from Noisy Measurements using Deep Learning with a Runge-Kutta Constraint](https://mlsanity.com/paper/2109.11446/) (2021)
- [Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2405.07839/) (2024)
- [Inferring the Langevin Equation with Uncertainty via Bayesian Neural Networks](https://mlsanity.com/paper/2402.01338/) (2024)

## 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.