arXiv subjects

Ethan Pickering

Publications and source records attributed to Ethan Pickering.

11 recordsLinked to original sources

arXiv2025

Biology-informed neural networks learn nonlinear representations from omics data to improve genomic prediction and interpretability

We extend biologically-informed neural networks (BINNs) for genomic prediction (GP) and selection (GS) in crops by integrating thousands of single-nucleotide polymorphisms (SNPs) with multi-omics measurements and prior biological knowledge. Traditional genotype-to-phenotype (G2P) models depend heavily on direct mappings that achieve only modest accuracy, forcing breeders to conduct large, costly field trials to maintain or marginally improve genetic gain. Models that incorporate intermediate molecular phenotypes such as gene expression can achieve higher predictive fit, but they remain impractical for GS since such data are unavailable at deployment or design time. BINNs overcome this limitation by encoding pathway-level inductive biases and leveraging multi-omics data only during training, while using genotype data alone during inference. Applied to maize gene-expression and multi-environment field-trial data, BINN improves rank-correlation accuracy by up to 56% within and across subpopulations under sparse-data conditions and nonlinearly identifies genes that GWAS/TWAS fail to uncover. With complete domain knowledge for a synthetic metabolomics benchmark, BINN reduces prediction error by 75% relative to conventional neural nets and correctly identifies the most important nonlinear pathway. Importantly, both cases show highly sensitive BINN latent variables correlate with the experimental quantities they represent, despite not being trained on them. This suggests BINNs learn biologically-relevant representations, nonlinear or linear, from genotype to phenotype. Together, BINNs establish a framework that leverages intermediate domain information to improve genomic prediction accuracy and reveal nonlinear biological relationships that can guide genomic selection, candidate gene selection, pathway enrichment, and gene-editing prioritization.

cs.LG↗

arXiv2025

Bispectral decomposition and energy transfer in a turbulent jet

We employ bispectral mode decomposition (BMD) to investigate coherent triadic interactions and nonlinear energy transfer in a subsonic turbulent jet. BMD extracts the flow structures corresponding to the dominant triadic interactions. We find a strong triadic correlation among the Kelvin-Helmholtz wavepacket, its conjugate, and the streaks. The most energetic streaks occur at the azimuthal wavenumber $m=2$, with the dominant contributing azimuthal wavenumber triad being $[m_1,m_2,m_3]=[1,1,2]$. The spectral energy budget reveals that nonlinear triadic interactions represent an energy loss to the streaks. Analysis across a wide range of frequencies and azimuthal wavenumbers identifies the direction of nonlinear energy transfer and the spatial regions where these transfers are most active. The turbulent jet exhibits a forward energy cascade in a global sense, though the direction of energy transfer varies locally. In the shear layer near the nozzle exit, triadic interactions between relatively smaller scales are dominant, leading to an inverse energy cascade. Farther downstream, beyond the end of the potential core, triadic interactions between larger scales dominate, resulting in a forward energy cascade.

physics.flu-dyn↗

arXiv2023

The effect of flight on a turbulent jet: coherent structure eduction and resolvent analysis

We study coherent structures in subsonic turbulent jets subject to a flight stream. A thorough characterisation of the effects of a flight stream on the turbulent field was recently performed by Maia et al. (2023) and fluctuation energy attenuations were observed over a broad range of frequencies and azimuthal wavenumbers. The Kelvin-Helmholtz, Orr and lift-up mecahnisms were all shown to be weakened by the flight stream. Here we expand upon that study and model the changes in the dynamics of jets in flight using global resolvent analysis. The resolvent model is found to correctly capture the main effects of the flight stream on the dynamics of coherent structures, which are educed from a large-eddy simulation database using spectral proper orthogonal decomposition (SPOD). Three modifications of note are: the damping of low-frequency streaky/Orr structures that carry most of the fluctuation energy; a degradation of the low-rank behaviour of the jet in frequencies where modal instability mechanisms are dominant; and a rank decrease at very low Strouhal numbers. The latter effect is underpinned by larger gain separations predicted by the resolvent analysis, due to a reduction in the wavelength of associated flow structures. This leads to a clearer relative dominance of streaky structures generated by the lift-up mechanism, despite the fact that the lift-up mechanism has been weakened with respect to the static jet.

physics.flu-dyn↗

arXiv2023

Jet mixing enhancement with Bayesian optimization, deep learning, and persistent data topology

We optimize the jet mixing using large eddy simulations (LES) at a Reynolds number of $3000$. Key methodological enablers consist of Bayesian optimization, a surrogate model enhanced by deep learning, and persistent data topology for physical interpretation. The mixing performance is characterized by an equivalent jet radius ($R_{\rm eq}$) derived from the streamwise velocity in a plane located $8$ diameters downstream. The optimization is performed in a 22-dimensional actuation space that comprises most known excitations. The plant benefits from a 22-dimensional actuation space that comprises most known excitations. This search space parameterizes distributed actuation imposed on the bulk flow and at the periphery of the nozzle in the streamwise and radial directions. The momentum flux measures the energy input of the actuation. The optimization quadruples the jet radius $R_{\rm eq}$ with a $7$-armed blooming jet after around $570$ evaluations. The control input requires $2\%$ momentum flux of the main flow, which is one order of magnitude lower than an ad hoc dual-mode excitation. Intriguingly, a pronounced suboptimum in the search space is associated with a double-helix jet, a new flow pattern. This jet pattern results in a mixing improvement comparable to the blooming jet. A state-of-the-art Bayesian optimization converges towards this double helix solution. The learning is accelerated and converges to another better optimum by including surrogate model trained along the optimization. Persistent data topology extracts the global and many local minima in the actuation space. These minima can be identified with flow patterns beneficial to the mixing.

physics.flu-dyn↗

arXiv2022

Information FOMO: The unhealthy fear of missing out on information. A method for removing misleading data for healthier models

Misleading or unnecessary data can have out-sized impacts on the health or accuracy of Machine Learning (ML) models. We present a Bayesian sequential selection method, akin to Bayesian experimental design, that identifies critically important information within a dataset, while ignoring data that is either misleading or brings unnecessary complexity to the surrogate model of choice. Our method improves sample-wise error convergence and eliminates instances where more data leads to worse performance and instabilities of the surrogate model, often termed sample-wise ``double descent''. We find these instabilities are a result of the complexity of the underlying map and linked to extreme events and heavy tails. Our approach has two key features. First, the selection algorithm dynamically couples the chosen model and data. Data is chosen based on its merits towards improving the selected model, rather than being compared strictly against other data. Second, a natural convergence of the method removes the need for dividing the data into training, testing, and validation sets. Instead, the selection metric inherently assesses testing and validation error through global statistics of the model. This ensures that key information is never wasted in testing or validation. The method is applied using both Gaussian process regression and deep neural network surrogate models.

cs.LG↗

arXiv2022

Discovering and forecasting extreme events via active learning in neural operators

Extreme events in society and nature, such as pandemic spikes, rogue waves, or structural failures, can have catastrophic consequences. Characterizing extremes is difficult as they occur rarely, arise from seemingly benign conditions, and belong to complex and often unknown infinite-dimensional systems. Such challenges render attempts at characterizing them as moot. We address each of these difficulties by combining novel training schemes in Bayesian experimental design (BED) with an ensemble of deep neural operators (DNOs). This model-agnostic framework pairs a BED scheme that actively selects data for quantifying extreme events with an ensemble of DNOs that approximate infinite-dimensional nonlinear operators. We find that not only does this framework clearly beat Gaussian processes (GPs) but that 1) shallow ensembles of just two members perform best; 2) extremes are uncovered regardless of the state of initial data (i.e. with or without extremes); 3) our method eliminates "double-descent" phenomena; 4) the use of batches of suboptimal acquisition points compared to step-by-step global optima does not hinder BED performance; and 5) Monte Carlo acquisition outperforms standard optimizers in high-dimensions. Together these conclusions form the foundation of an AI-assisted experimental infrastructure that can efficiently infer and pinpoint critical situations across many domains, from physical to societal systems.

cs.LG↗

arXiv2022

Structure and Distribution Metric for Quantifying the Quality of Uncertainty: Assessing Gaussian Processes, Deep Neural Nets, and Deep Neural Operators for Regression

We propose two bounded comparison metrics that may be implemented to arbitrary dimensions in regression tasks. One quantifies the structure of uncertainty and the other quantifies the distribution of uncertainty. The structure metric assesses the similarity in shape and location of uncertainty with the true error, while the distribution metric quantifies the supported magnitudes between the two. We apply these metrics to Gaussian Processes (GPs), Ensemble Deep Neural Nets (DNNs), and Ensemble Deep Neural Operators (DNOs) on high-dimensional and nonlinear test cases. We find that comparing a model's uncertainty estimates with the model's squared error provides a compelling ground truth assessment. We also observe that both DNNs and DNOs, especially when compared to GPs, provide encouraging metric values in high dimensions with either sparse or plentiful data.

cs.LG↗

arXiv2021

Efficient global resolvent analysis via the one-way Navier-Stokes equations. Part 1. Forced response

Resolvent analysis is a powerful tool for modeling and analyzing turbulent flows and in particular provides an approximation of coherent flow structures. Despite recent algorithmic advances, computing resolvent modes for flows with more than one inhomogeneous spatial coordinate remains computationally expensive. In this two-part paper, we show how efficient and accurate approximations of resolvent modes can be obtained using a well-posed spatial marching method for flows that contain a slowly varying direction. In this first part of the paper, we derive a well-posed and convergent one-way equation describing the downstream-traveling waves supported by the linearized Navier-Stokes equations. Integrating these equations, which requires significantly less CPU and memory resources than a direct solution of the linearized Navier-Stokes equations, approximates the action of the resolvent operator on a forcing vector. This capability is leveraged in part 2 of the paper to compute approximate resolvent modes. The method is validated and demonstrated using the examples of a simple acoustics problem and a supersonic turbulent jet.

physics.flu-dyn↗

arXiv2021

Resolvent-based modeling of turbulent jet noise

Resolvent analysis has demonstrated encouraging results for modeling coherent structures in jets when compared against their data-educed counterparts from high-fidelity large-eddy simulations (LES). We formulate resolvent analysis as an acoustic analogy that relates the near-field resolvent forcing to the near- and far-field pressure. We use an LES database of round, isothermal, Mach 0.9 and 1.5 jets to produce an ensemble of realizations for the acoustic field that we project onto a limited set of resolvent modes. In the near-field, we perform projections on a restricted acoustic output domain, $r/D = [5,6]$, while the far-field projections are performed on a Kirchhoff surface comprising a 100-diameter arc centered at the nozzle. This allows the LES realizations to be expressed in the resolvent basis via a data-deduced, low-rank, cross-spectral density matrix. We find that a single resolvent mode reconstructs the most energetic regions of the acoustic field across Strouhal numbers, $St = [0-1]$, and azimuthal wavenumbers, $m=[0,2]$. Finally, we present a simple function that results in a rank-1 resolvent model agreeing within 2dB of the peak noise for both jets.

physics.flu-dyn↗

arXiv2021

Optimal eddy viscosity for resolvent-based models of coherent structures in turbulent jets

Response modes computed via linear resolvent analysis of a turbulent mean-flow field have been shown to qualitatively capture characteristics of the observed turbulent coherent structures in both wall-bounded and free shear flows. To make such resolvent models predictive, the nonlinear forcing term must be closed. Strategies to do so include imposing self-consistent sets of triadic interactions, proposing various source models, or through turbulence modelling. For the latter, several investigators have proposed using the mean-field eddy viscosity acting linearly on the fluctuation field. In this study, a data-driven approach is taken to quantitatively improve linear resolvent models by deducing an optimal eddy-viscosity field that maximizes the projection of the dominant resolvent mode to the energy-optimal coherent structure educed using spectral proper orthogonal decomposition (SPOD) of data from high-fidelity simulations. We use large-eddy simulation databases for round isothermal jets at subsonic, transonic, and supersonic conditions and show that the optimal eddy viscosity substantially improves the alignment between resolvent and SPOD modes, reaching over 90% alignment at those frequencies where the jet exhibits a low-rank response. We then consider a fixed model for the eddy viscosity and show that with the calibration of a single constant, the results are generally close to the optimal one. In particular, the use of a standard Reynolds-Averaged-Navier-Stokes (RANS) eddy-viscosity resolvent model, with a single coefficient, provides substantial agreement between SPOD and resolvent modes for three turbulent jets and across the most energetic wavenumbers and frequencies.

physics.flu-dyn↗

arXiv2020

Lift-up, Kelvin-Helmholtz and Orr mechanisms in turbulent jets

Three amplification mechanisms present in turbulent jets, namely lift-up, Kelvin-Helmholtz, and Orr, are characterized via global resolvent analysis and spectral proper orthogonal decomposition (SPOD) over a range of Mach numbers. The lift-up mechanism was recently identified in turbulent jets via local analysis by Nogueira et al. (J. Fluid Mech., vol. 873, 2019, pp. 211-237) at low Strouhal number ($St$) and non-zero azimuthal wavenumbers ($m$). In these limits, a global SPOD analysis of data from high-fidelity simulations reveals streamwise vortices and streaks similar to those found in turbulent wall-bounded flows. These structures are in qualitative agreement with the global resolvent analysis, which shows that they are a response to upstream forcing of streamwise vorticity near the nozzle exit. Analysis of mode shapes, component-wise amplitudes, and sensitivity analysis distinguishes the three mechanisms and the regions of frequency-wavenumber space where each dominates, finding lift-up to be dominant as $St/m \rightarrow 0$. Finally, SPOD and resolvent analyses of localized regions show that the lift-up mechanism is present throughout the jet, with a dominant azimuthal wavenumber inversely proportional to streamwise distance from the nozzle, with streaks of azimuthal wavenumber exceeding five near the nozzle, and wavenumbers one and two most energetic far downstream of the potential core.

physics.flu-dyn↗