Discovering stochastic dynamical equations from biological time series data

• URL: http://arxiv.org/abs/2205.02645v5
• Date: Sat, 17 Feb 2024 06:53:08 GMT
• Title: Discovering stochastic dynamical equations from biological time series data
• Authors: Arshed Nabeel, Ashwin Karichannavar, Shuaib Palathingal, Jitesh Jhawar, David B. Br\"uckner, Danny Raj M., Vishwesha Guttal
• Abstract summary: We present an equation discovery methodology that takes time series data as an input, analyses fine scale fluctuations and interpretable SDEs. We make the method available as an easy-to-use, open-source Python package, PyDaddy (Python for Dynamics Driven Data).
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Stochastic differential equations (SDEs) are an important framework to model dynamics with randomness, as is common in most biological systems. The inverse problem of integrating these models with empirical data remains a major challenge. Here, we present an equation discovery methodology that takes time series data as an input, analyses fine scale fluctuations and outputs an interpretable SDE that can correctly capture long-time dynamics of data. We achieve this by combining traditional approaches from stochastic calculus literature with state-of-the-art equation discovery techniques. We validate our approach on synthetic datasets, and demonstrate the generality and applicability of the method on two real-world datasets of vastly different spatiotemporal scales: (i) collective movement of fish school where stochasticity plays a crucial role, and (ii) confined migration of a single cell, primarily following a relaxed oscillation. We make the method available as an easy-to-use, open-source Python package, PyDaddy (Python Library for Data Driven Dynamics).

Related papers

• Learning Controlled Stochastic Differential Equations [61.82896036131116]
  This work proposes a novel method for estimating both drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled differential equations with non-uniform diffusion. We provide strong theoretical guarantees, including finite-sample bounds for (L2), (Linfty), and risk metrics, with learning rates adaptive to coefficients' regularity. Our method is available as an open-source Python library.
  arXiv  Detail & Related papers  (2024-11-04T11:09:58Z)
• HyperSINDy: Deep Generative Modeling of Nonlinear Stochastic Governing Equations [5.279268784803583]
  We introduce HyperSINDy, a framework for modeling dynamics via a deep generative model of sparse governing equations from data. Once trained, HyperSINDy generates dynamics via a differential equation whose coefficients are driven by a white noise. In experiments, HyperSINDy recovers ground truth governing equations, with learnedity scaling to match that of the data.
  arXiv  Detail & Related papers  (2023-10-07T14:41:59Z)
• Score-based Continuous-time Discrete Diffusion Models [102.65769839899315]
  We extend diffusion models to discrete variables by introducing a Markov jump process where the reverse process denoises via a continuous-time Markov chain. We show that an unbiased estimator can be obtained via simple matching the conditional marginal distributions. We demonstrate the effectiveness of the proposed method on a set of synthetic and real-world music and image benchmarks.
  arXiv  Detail & Related papers  (2022-11-30T05:33:29Z)
• D-CIPHER: Discovery of Closed-form Partial Differential Equations [80.46395274587098]
  We propose D-CIPHER, which is robust to measurement artifacts and can uncover a new and very general class of differential equations. We further design a novel optimization procedure, CoLLie, to help D-CIPHER search through this class efficiently.
  arXiv  Detail & Related papers  (2022-06-21T17:59:20Z)
• Capturing Actionable Dynamics with Structured Latent Ordinary Differential Equations [68.62843292346813]
  We propose a structured latent ODE model that captures system input variations within its latent representation. Building on a static variable specification, our model learns factors of variation for each input to the system, thus separating the effects of the system inputs in the latent space.
  arXiv  Detail & Related papers  (2022-02-25T20:00:56Z)
• Discovery of Nonlinear Dynamical Systems using a Runge-Kutta Inspired Dictionary-based Sparse Regression Approach [9.36739413306697]
  We blend machine learning and dictionary-based learning with numerical analysis tools to discover governing differential equations. We obtain interpretable and parsimonious models which are prone to generalize better beyond the sampling regime. We discuss its extension to governing equations, containing rational nonlinearities that typically appear in biological networks.
  arXiv  Detail & Related papers  (2021-05-11T08:46:51Z)
• Inference of Stochastic Dynamical Systems from Cross-Sectional Population Data [8.905677748354364]
  Inferring the driving equations of a dynamical system from population or time-course data is important in several scientific fields such as biochemistry, epidemiology, financial mathematics and many others. In this work, we deduce and then computationally estimate the Fokker-Planck equation which describes the evolution of the population's probability density, based on differential equations. Then, following the USDL approach, we project the Fokker-Planck equation to a proper set of test functions, transforming it into a linear system of equations.
  arXiv  Detail & Related papers  (2020-12-09T14:02:29Z)
• ImitationFlow: Learning Deep Stable Stochastic Dynamic Systems by Normalizing Flows [29.310742141970394]
  We introduce ImitationFlow, a novel Deep generative model that allows learning complex globally stable, nonlinear dynamics. We show the effectiveness of our method with both standard datasets and a real robot experiment.
  arXiv  Detail & Related papers  (2020-10-25T14:49:46Z)
• The data-driven physical-based equations discovery using evolutionary approach [77.34726150561087]
  We describe the algorithm for the mathematical equations discovery from the given observations data. The algorithm combines genetic programming with the sparse regression. It could be used for governing analytical equation discovery as well as for partial differential equations (PDE) discovery.
  arXiv  Detail & Related papers  (2020-04-03T17:21:57Z)
• Learning Stochastic Behaviour from Aggregate Data [52.012857267317784]
  Learning nonlinear dynamics from aggregate data is a challenging problem because the full trajectory of each individual is not available. We propose a novel method using the weak form of Fokker Planck Equation (FPE) to describe the density evolution of data in a sampled form. In such a sample-based framework we are able to learn the nonlinear dynamics from aggregate data without explicitly solving the partial differential equation (PDE) FPE.
  arXiv  Detail & Related papers  (2020-02-10T03:20:13Z)
• Data-Driven Discovery of Coarse-Grained Equations [0.0]
  Multiscale modeling and simulations are two areas where learning on simulated data can lead to such discovery. We replace the human discovery of such models with a machine-learning strategy based on sparse regression that can be executed in two modes. A series of examples demonstrates the accuracy, robustness, and limitations of our approach to equation discovery.
  arXiv  Detail & Related papers  (2020-01-30T23:41:37Z)

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.