Probabilistic grammars improve equation discovery from data.
problem Discovering scientific laws from data using equations.
method Proposed probabilistic context-free grammars to encode soft constraints and a Monte-Carlo algorithm.
result Probabilistic grammars lead to more efficient equation discovery.
Paper discovers structural dynamics equations from only acceleration data.
problem Discovering equations from only acceleration measurements in structural dynamics.
method Library-based approach with Approximate Bayesian Computation (ABC) prioritizing parsimonious models.
result Efficacy demonstrated in four structural dynamics examples, including linear and nonlinear systems.
Paper discovers governing equations from data using differential invariants.
problem Discovering partial differential equations from data is challenging.
method The paper proposes a pipeline based on differential invariants to reduce the search space and adhere to symmetry.
result DI-SINDy method outperforms other symmetry-informed methods in PDE discovery.
Automates discovery of interpretable Lagrangians from data.
problem Lack of interpretable Lagrangian discovery methods.
method Data-driven machine learning algorithm to derive interpretable Lagrangians.
result Automated discovery of interpretable Lagrangians and conservation laws.
Quantum model discovery uses DQCs to solve equations from data.
problem Discovering differential equations from data using quantum computing.
method Differentiable quantum circuits (DQCs) to solve parameterized equations, regression on data and equations.
result Successful parameter inference and equation discovery on various systems.
Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning on simulated data can lead to such discovery. In both, the data are generated w…
Bayesian autoencoders discover physics from noisy data.
problem Challenges in identifying governing equations and coordinates from noisy, low-data real-world data.
method Bayesian SINDy autoencoders with hierarchical Bayesian sparsifying prior and adaptive empirical Bayesian method.
result Better physics discovery with lower data and fewer training epochs, along with valid uncertainty quantification.
Paper discovers differential equations from data using neural networks and Bayesian methods.
problem Discovering differential equations from datasets using machine learning.
method Integrates neural network-based surrogates with Sparse Bayesian Learning (SBL).
result Proposes a robust model discovery algorithm and a Physics Informed Normalizing Flow (PINF).
Automated PDE discovery from multiple noisy experiments.
problem Inherent variability in experiments makes single experiment inference unreliable.
method Randomised adaptive group Lasso sparsity estimator in deep learning framework.
result More generalizable PDEs found from multiple datasets.
The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery (S3d), decides which physical terms are necessary and which can be removed (because they are physically n…
New methods discover causal relationships from multiple related data views.
problem Causal discovery from non-Gaussian data.
method Multi-view linear Structural Equation Model (SEM) with weak assumptions.
result Identifiability of acyclic SEMs and successful causal graph estimation.
Deep learning improves model discovery from sparse sensor data.
problem Improving physical understanding and predictions from coarse, non-grid sampled data.
method Physics-informed neural networks and automatic differentiation.
result Deep learning can recover underlying equations from sparse, non-grid data.
New method recovers PDEs from noisy data, even when conditions are violated.
problem Discovering PDEs from noisy, limited data.
method Randomized adaptive Lasso integrated into DeepMod.
result Recovery of PDEs with higher noise-to-sample ratios and single hyperparameters.
A new method discovers equations from data using Bayesian and kernel techniques.
problem Discovering equations from data is hard due to sparsity and noise.
method Kernel regression for function estimation and Bayesian spike-and-slab prior for uncertainty quantification.
result KBASS method outperforms state-of-the-art methods on benchmark tasks.
Bayesian method discovers PDEs with variable coefficients robustly.
problem Discovering PDEs from noisy data is challenging.
method Bayesian sparse learning with tBGL-SS and Gibbs sampler.
result Method enhances robustness and model selection criteria.
A new algorithm speeds up sparse regression for discovering equations from data.
problem Learning governing equations from vast data with unsatisfying descriptions.
method SPRINT: a fast algorithm using bisection and analytic bounds to identify optimal rank-1 modifications.
result A calculation that would take millions of years can be done in a day.
Data-driven discovery of differential equations has been an emerging research topic. We propose a novel algorithm subsampling-based threshold sparse Bayesian regression (SubTSBR) to tackle high noise and outliers. The subsampling technique is used for improving the accuracy of the Bayesian learning algorithm. It has tw…
SIP framework discovers governing equations in uncertain systems.
problem Discovering governing equations in systems with input variability and noisy data.
method SIP framework treats unknown coefficients as random variables and infers their posterior distribution by minimizing Kullback-Leibler divergence.
result SIP consistently identifies correct equations and lowers coefficient error by 82% relative to SINDy.
The paper develops CI tests for causal discovery in SDEs.
problem Inferring causal structure from stochastic dynamical systems.
method Developed CI constraints and a CI test for SDEs.
result Proposed CI test outperforms existing methods.
V-SysId identifies keypoints and 3D system from unlabeled videos.
problem Identifying keypoints and 3D system from unlabeled videos.
method Alternates between parameter estimation and extrinsic camera calibration, using motion equations as weak supervision.
result Utility of the approach demonstrated across various settings.
A new method ODR-BINDy improves model discovery from noisy data.
problem Discovering models from noisy datasets with error-in-variable problem.
method ODR-BINDy uses orthogonal distance regression with Bayesian model selection.
result ODR-BINDy consistently outperforms existing methods in recovering correct models.
Equation discovery methods enable modelers to combine domain-specific knowledge and system identification to construct models most suitable for a selected modeling task. The method described and evaluated in this paper can be used as a nonlinear system identification method for gray-box modeling. It consists of two int…
Proposes KAR for nonlinear causal discovery using kernel methods.
problem Learning causal relationships in nonlinear settings.
method Kernel anchor regression (KAR) with improved three-stage nonparametric regression.
result KAR outperforms existing methods in nonlinear causal discovery.
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this second part of our two-part treatise, we focus on the problem of data-driven discovery of …
Develops a model for causal discovery in path spaces.
problem Discover causal relationships in path spaces using asymmetric independence.
method Theory linking E-separation in DMGs to conditional independence in SDEs, proving global Markov property, characterizing equivalence classes of graphs.
result Each equivalence class of graphs has a greatest element as a parsimonious representation, which can be identified from data.
New method discovers symmetries in differential equations from data.
problem Directly identifying Lie symmetries from scattered data without explicit equations.
method Numerical scheme using manifold learning and linear system construction.
result Accuracy and robustness demonstrated in various differential equations.
New RL formulation for maximizing maximum reward in molecule generation.
problem Traditional RL frameworks do not fit real-world applications like drug discovery.
method Formulated a new objective function to maximize maximum reward, derived Bellman equation, introduced operators, and proved convergence.
result Achieved state-of-the-art results in molecule generation.
Discover equations from data using neural networks with constraints.
problem Discover equations from noisy data without theoretical derivation.
method Solve constrained optimization problem with penalty or trust-region barrier methods.
result Constrained method outperforms penalty method for higher noise levels or fewer collocation points.
Bayesian method learns PDEs from noisy data.
problem Discovering PDEs from noisy data.
method Combining variational Bayes and sparse linear regression.
result Proposes a new method to discover PDEs accurately.
In recent years, data-driven methods have been developed to learn dynamical systems and partial differential equations (PDE). The goal of such work is discovering unknown physics and the corresponding equations. However, prior to achieving this goal, major challenges remain to be resolved, including learning PDE under …
New method for causal discovery using peeling algorithms for various data types.
problem Challenges in causal discovery due to unmeasured confounders.
method Two peeling algorithms (bottom-up and top-down) for causal discovery with generalized structural equation models.
result Valid discovery of causal relationships and parent-child effects in diverse data types.
BCD Nets use variational inference to estimate DAGs with uncertainty.
problem Uncertainty in inferring causal graphs from limited data.
method Variational inference framework for Bayesian DAG estimation.
result BCD Nets outperform maximum-likelihood methods in low data regimes.
Bayesian framework discovers interpretable Lagrangian from data.
problem Discovering physical laws from limited data.
method Sparse Bayesian approach for learning interpretable Lagrangian.
result Automates Hamiltonian discovery from Lagrangian and provides ODE/PDE descriptions.
Interpretable framework evaluates structure learning methods for causal discovery from observational data.
problem Evaluation of structure learning methods under assumption violations in causal discovery.
method Six-dimensional evaluation metric (DOS) tailored for causal discovery.
result Amortized causal discovery delivers results with high proximity to the optimal solution.
Efficient algorithms decide algebraic constraints of causal graphs.
problem Distinguish causal graphs with latent confounders.
method Study algebraic constraints and propose efficient algorithms.
result Decide equivalence or subset of algebraic constraints.
BLADE uses Bayesian methods to discover complex systems from scarce data.
problem Efficiently discovering governing equations of complex dynamical systems from limited data.
method Combines replica-exchange stochastic gradient Langevin Monte Carlo with active learning.
result Reduces measurement requirements by 60% for Lotka-Volterra and 40% for Burgers' equation.
We introduce DeepMoD, a Deep learning based Model Discovery algorithm. DeepMoD discovers the partial differential equation underlying a spatio-temporal data set using sparse regression on a library of possible functions and their derivatives. A neural network approximates the data and constructs the function library, b…
New method discovers causal relationships in large-scale data.
problem Discovering causal relationships in large datasets with thousands of variables.
method Factor Directed Acyclic Graphs (f-DAGs) combined with continuous optimization.
result Achieved causal discovery on thousands of variables.
We introduce a model for causal structure learning from multivariate functional data, even when graphs have cycles.
problem Discovering causal relationships from multivariate functional data with cycles.
method Functional linear structural equation model with a low-dimensional causal embedded space.
result The proposed model is causally identifiable under standard assumptions.
TSCD is an algorithm for causal discovery using second-order statistics.
problem Causal discovery
method Tensor-based Second-order Causal Discovery (TSCD)
result Identifiable causal order and parameters from logarithmic number of interventions
Kernel method learns PDEs from noisy data.
problem Discovering and solving PDEs from noisy data.
method Kernel smoothing, regression, and operator learning.
result Competitive performance compared to state-of-the-art algorithms.
A method uses non-autonomous equations to classify time signals efficiently.
problem Time signal classification with minimal parameters and high accuracy.
method Develops a framework using non-autonomous dynamical equations to classify time signals.
result The method achieves comparable accuracy with fewer parameters than existing methods.
Extracts coarse-grained PDEs from microscopic simulations.
problem Discovering effective PDEs for macro-scale processes from microscopic data.
method Combining neural networks with equation-free numerics and data-driven approaches.
result Efficiently discovers macro-scale PDEs from microscopic simulations.
Bayesian framework for robust model discovery from noisy data.
problem Robust model discovery from noisy, sparse and irregular observations of nonlinear systems.
method Bayesian differential programming using Hamiltonian Monte Carlo and sparsity-promoting priors.
result Efficient inference of posterior distributions over plausible models with quantified uncertainty.
New framework discovers PDEs from sparse, noisy data.
problem Discovering PDEs with high-order derivatives and heterogeneous parameters.
method Combines deep-learning and integral form to handle sparse and noisy data.
result More robust and accurate compared to existing methods.
These are lecture notes for a short winter course at the Department of Mathematics, University of Coimbra, Portugal, December 6--8, 2018. The course was part of the 13th International Young Researchers Workshop on Geometry, Mechanics and Control. In three lectures I trace the work of three heroes of mathematics and mec…
Automates discovering PDEs from data in dynamical systems.
problem Identifying PDEs from data in dynamical systems is challenging.
method ARGOS-RAL framework using sparse regression with recurrent adaptive lasso.
result ARGOS-RAL effectively identifies PDEs from noisy and non-uniformly distributed data.
Machine learning (ML) and artificial intelligence (AI) algorithms are now being used to automate the discovery of physics principles and governing equations from measurement data alone. However, positing a universal physical law from data is challenging without simultaneously proposing an accompanying discrepancy model…