Browse
Submit Data
Databases
API
Help

Dataset Information

28 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Stability selection enables robust learning of differential equations from limited noisy data.

ABSTRACT: We present a statistical learning framework for robust identification of differential equations from noisy spatio-temporal data. We address two issues that have so far limited the application of such methods, namely their robustness against noise and the need for manual parameter tuning, by proposing stability-based model selection to determine the level of regularization required for reproducible inference. This avoids manual parameter tuning and improves robustness against noise in the data. Our stability selection approach, termed PDE-STRIDE, can be combined with any sparsity-promoting regression method and provides an interpretable criterion for model component importance. We show that the particular combination of stability selection with the iterative hard-thresholding algorithm from compressed sensing provides a fast and robust framework for equation inference that outperforms previous approaches with respect to accuracy, amount of data required, and robustness. We illustrate the performance of PDE-STRIDE on a range of simulated benchmark problems, and we demonstrate the applicability of PDE-STRIDE on real-world data by considering purely data-driven inference of the protein interaction network for embryonic polarization in Caenorhabditis elegans. Using fluorescence microscopy images of C. elegans zygotes as input data, PDE-STRIDE is able to learn the molecular interactions of the proteins.

SUBMITTER: Maddu S

PROVIDER: S-EPMC9199075 | biostudies-literature |

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Similar Datasets

Learning partial differential equations for biological transport models from noisy spatio-temporal data.

Project description:We investigate methods for learning partial differential equation (PDE) models from spatio-temporal data under biologically realistic levels and forms of noise. Recent progress in learning PDEs from data have used sparse regression to select candidate terms from a denoised set of data, including approximated partial derivatives. We analyse the performance in using previous methods to denoise data for the task of discovering the governing system of PDEs. We also develop a novel methodology that uses artificial neural networks (ANNs) to denoise data and approximate partial derivatives. We test the methodology on three PDE models for biological transport, i.e. the advection-diffusion, classical Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) and nonlinear Fisher-KPP equations. We show that the ANN methodology outperforms previous denoising methods, including finite differences and both local and global polynomial regression splines, in the ability to accurately approximate partial derivatives and learn the correct PDE model.

| S-EPMC7069483 | biostudies-literature

Learning data-driven discretizations for partial differential equations.

Project description:The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length- and timescales. Often, it is computationally intractable to resolve the finest features in the solution. The only recourse is to use approximate coarse-grained representations, which aim to accurately represent long-wavelength dynamics while properly accounting for unresolved small-scale physics. Deriving such coarse-grained equations is notoriously difficult and often ad hoc. Here we introduce data-driven discretization, a method for learning optimized approximations to PDEs based on actual solutions to the known underlying equations. Our approach uses neural networks to estimate spatial derivatives, which are optimized end to end to best satisfy the equations on a low-resolution grid. The resulting numerical methods are remarkably accurate, allowing us to integrate in time a collection of nonlinear equations in 1 spatial dimension at resolutions 4× to 8× coarser than is possible with standard finite-difference methods.

| S-EPMC6681734 | biostudies-literature

Discovery of Partial Differential Equations from Highly Noisy and Sparse Data with Physics-Informed Information Criterion.

Project description:Data-driven discovery of partial differential equations (PDEs) has recently made tremendous progress, and many canonical PDEs have been discovered successfully for proof of concept. However, determining the most proper PDE without prior references remains challenging in terms of practical applications. In this work, a physics-informed information criterion (PIC) is proposed to measure the parsimony and precision of the discovered PDE synthetically. The proposed PIC achieves satisfactory robustness to highly noisy and sparse data on 7 canonical PDEs from different physical scenes, which confirms its ability to handle difficult situations. The PIC is also employed to discover unrevealed macroscale governing equations from microscopic simulation data in an actual physical scene. The results show that the discovered macroscale PDE is precise and parsimonious and satisfies underlying symmetries, which facilitates understanding and simulation of the physical process. The proposition of the PIC enables practical applications of PDE discovery in discovering unrevealed governing equations in broader physical scenes.

| S-EPMC10198462 | biostudies-literature

Robust meta gradient learning for high-dimensional data with noisy-label ignorance.

Project description:Large datasets with noisy labels and high dimensions have become increasingly prevalent in industry. These datasets often contain errors or inconsistencies in the assigned labels and introduce a vast number of predictive variables. Such issues frequently arise in real-world scenarios due to uncertainties or human errors during data collection and annotation processes. The presence of noisy labels and high dimensions can significantly impair the generalization ability and accuracy of trained models. To address the above issues, we introduce a simple-structured penalized γ-divergence model and a novel meta-gradient correction algorithm and establish the foundations of these two modules based on rigorous theoretical proofs. Finally, comprehensive experiments are conducted to validate their effectiveness in detecting noisy labels and mitigating the curse of dimensionality and suggest that our proposed model and algorithm can achieve promising outcomes. Moreover, we open-source our codes and distinctive datasets on GitHub (refer to https://github.com/DebtVC2022/Robust_Learning_with_MGC).

| S-EPMC10712856 | biostudies-literature

Learning partial differential equations via data discovery and sparse optimization.

Project description:We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.

| S-EPMC5312119 | biostudies-literature

Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression.

Project description:Machine learning offers an intriguing alternative to first-principle analysis for discovering new physics from experimental data. However, to date, purely data-driven methods have only proven successful in uncovering physical laws describing simple, low-dimensional systems with low levels of noise. Here we demonstrate that combining a data-driven methodology with some general physical principles enables discovery of a quantitatively accurate model of a non-equilibrium spatially extended system from high-dimensional data that is both noisy and incomplete. We illustrate this using an experimental weakly turbulent fluid flow where only the velocity field is accessible. We also show that this hybrid approach allows reconstruction of the inaccessible variables - the pressure and forcing field driving the flow.

| S-EPMC8163752 | biostudies-literature

Deep learning enables robust assessment and selection of human blastocysts after in vitro fertilization.

Project description:Visual morphology assessment is routinely used for evaluating of embryo quality and selecting human blastocysts for transfer after in vitro fertilization (IVF). However, the assessment produces different results between embryologists and as a result, the success rate of IVF remains low. To overcome uncertainties in embryo quality, multiple embryos are often implanted resulting in undesired multiple pregnancies and complications. Unlike in other imaging fields, human embryology and IVF have not yet leveraged artificial intelligence (AI) for unbiased, automated embryo assessment. We postulated that an AI approach trained on thousands of embryos can reliably predict embryo quality without human intervention. We implemented an AI approach based on deep neural networks (DNNs) to select highest quality embryos using a large collection of human embryo time-lapse images (about 50,000 images) from a high-volume fertility center in the United States. We developed a framework (STORK) based on Google's Inception model. STORK predicts blastocyst quality with an AUC of >0.98 and generalizes well to images from other clinics outside the US and outperforms individual embryologists. Using clinical data for 2182 embryos, we created a decision tree to integrate embryo quality and patient age to identify scenarios associated with pregnancy likelihood. Our analysis shows that the chance of pregnancy based on individual embryos varies from 13.8% (age ≥41 and poor-quality) to 66.3% (age <37 and good-quality) depending on automated blastocyst quality assessment and patient age. In conclusion, our AI-driven approach provides a reproducible way to assess embryo quality and uncovers new, potentially personalized strategies to select embryos.

| S-EPMC6550169 | biostudies-literature

Data-driven discovery of partial differential equations.

Project description:We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg-de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable.

| S-EPMC5406137 | biostudies-literature

Machine Learning Enables Selection of Epistatic Enzyme Mutants for Stability Against Unfolding and Detrimental Aggregation.

Project description:Machine learning (ML) has pervaded most areas of protein engineering, including stability and stereoselectivity. Using limonene epoxide hydrolase as the model enzyme and innov'SAR as the ML platform, comprising a digital signal process, we achieved high protein robustness that can resist unfolding with concomitant detrimental aggregation. Fourier transform (FT) allows us to take into account the order of the protein sequence and the nonlinear interactions between positions, and thus to grasp epistatic phenomena. The innov'SAR approach is interpolative, extrapolative and makes outside-the-box, predictions not found in other state-of-the-art ML or deep learning approaches. Equally significant is the finding that our approach to ML in the present context, flanked by advanced molecular dynamics simulations, uncovers the connection between epistatic mutational interactions and protein robustness.

| S-EPMC7984044 | biostudies-literature

Estimating selection on synonymous codon usage from noisy experimental data.

Project description:A key goal in molecular evolution is to extract mechanistic insights from signatures of selection. A case study is codon usage, where despite many recent advances and hypotheses, two longstanding problems remain: the relative contribution of selection and mutation in determining codon frequencies and the relative contribution of translational speed and accuracy to selection. The relevant targets of selection--the rate of translation and of mistranslation of a codon per unit time in the cell--can only be related to mechanistic properties of the translational apparatus if the number of transcripts per cell is known, requiring use of gene expression measurements. Perhaps surprisingly, different gene-expression data sets yield markedly different estimates of selection. We show that this is largely due to measurement noise, notably due to differences between studies rather than instrument error or biological variability. We develop an analytical framework that explicitly models noise in expression in the context of the population-genetic model. Estimates of mutation and selection strength in budding yeast produced by this method are robust to the expression data set used and are substantially higher than estimates using a noise-blind approach. We introduce per-gene selection estimates that correlate well with previous scoring systems, such as the codon adaptation index, while now carrying an evolutionary interpretation. On average, selection for codon usage in budding yeast is weak, yet our estimates show that genes range from virtually unselected to average per-codon selection coefficients above the inverse population size. Our analytical framework may be generally useful for distinguishing biological signals from measurement noise in other applications that depend upon measurements of gene expression.

| S-EPMC3649678 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

Tweets

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data