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Using active learning to improve quasar identification for the DESI spectra processing pipeline

The Dark Energy Spectroscopic Instrument (DESI) survey uses an automatic spectral classification pipeline to classify spectra. QuasarNET is a convolutional neural network used as part of this pipeline originally trained using data from the Baryon Oscillation Spectroscopic Survey (BOSS). In this paper we implement an active learning algorithm to optimally select spectra to use for training a new version of the QuasarNET weights file using only DESI data, with the goal of improving classification accuracy. This active learning algorithm includes a novel outlier rejection step using a Self-Organizing Map to ensure we label spectra representative of the larger quasar sample observed in DESI. We perform two iterations of the active learning pipeline, assembling a final dataset of 5600 labeled spectra, a small subset of the approximately 1.3 million quasar targets in DESI's Data Release 1. When splitting the spectra into training and validation subsets we achieve similar performance to the previously trained weights file in completeness and purity calculated on the validation dataset but do so with less than one tenth of the amount of training data. The new weights also more consistently classify objects in the same way when used on unlabeled data compared to the old weights file. In the process of improving QuasarNET's classification accuracy we discovered a systemic error in QuasarNET's redshift estimation and used our findings to improve our understanding of QuasarNET's redshifts.

Machine learning↗

Towards fully predictive gyrokinetic full- f simulations: validation and triangularity studies in TCV

Designing economical magnetic confinement fusion power plants motivates computational tools that can estimate plasma behavior from engineering parameters without direct reliance on experimental measurement of the plasma profiles. In this work, we present full-f global long-wavelength gyrokinetic simulations of edge and scrape-off layer turbulence in tokamaks that use only magnetic geometry, heating power, and particle inventory as inputs. Unlike many modeling approaches that employ free parameters fitted to experimental data, raising uncertainties when extrapolating to reactor scales. This approach directly simulates turbulence and resulting profiles through gyrokinetics without such empirical adjustments. This is achieved via an adaptive sourcing algorithm in Gkeyll that strictly controls energy injection and emulates particle sourcing due to neutral recycling. We show that the simulated kinetic profiles compare reasonably well with Thomson scattering and Langmuir probe data for Tokamak á Configuration Variable (TCV) discharge #65125, and that the simulations reproduce characteristic features such as blob transport and self-organized electric fields. Applying the same framework to study triangularity effects suggests mechanisms contributing to the improved confinement reported for negative triangularity (NT). Simulations of TCV discharges #65125 and #65130 indicate that NT increases the E x B flow shear (by about 20% in these cases), which correlates with reduced turbulent losses and a modest change in the distribution of power exhaust to the vessel wall. While the physical models contain approximations that can be refined in future work, the predictive capability demonstrated here, evolving multiple profile relaxation times with kinetic electron and ion models in hundreds of GPU hours, indicates the feasibility of using Gkeyll to support design studies of fusion devices.

Hoffmann, Antoine Cyril David [Princeton Plasma Ph↗

Dark Energy Survey Year 6 results: Clustering redshifts and importance sampling of self-organized-maps 𝑛⁡(𝑧) realizations for 3 × 2 ⁢pt samples

This work is part of a series establishing the redshift framework for the 3 × 2 ⁢pt analysis of the Dark Energy Survey Year 6 (DES Y6). For DES Y6, photometric redshift distributions are estimated using self-organizing maps (SOMs), calibrated with spectroscopic and many-band photometric data. To overcome limitations from color-redshift degeneracies and incomplete spectroscopic coverage, we enhance this approach by incorporating clustering-based redshift constraints (clustering-z, or WZ) from angular cross-correlations with BOSS and eBOSS galaxies and eBOSS quasar samples. We define a WZ likelihood and apply importance sampling to a large ensemble of SOM-derived 𝑛⁡(𝑧) realizations, selecting those consistent with the clustering measurements to produce a posterior sample for each lens and source bin. The analysis uses angular scales corresponding to 1.5–5 Mpc to optimize signal-to-noise ratio while mitigating modeling uncertainties and marginalizes over redshift-dependent galaxy bias and other systematics informed by the N-body simulation CARDINAL . While a sparser spectroscopic reference sample limits WZ constraining power at 𝑧 >1.1, particularly for source bins, we demonstrate that combining SOM with WZ improves redshift accuracy and enhances the overall cosmological constraining power of DES Y6. As a result, we estimate an improvement in 𝑆 8 of approximately 10% for cosmic shear and 3 ×2⁢pt analysis, primarily due to the WZ calibration of the source samples.

Cosmological parameters↗

Dark Energy Survey Year 6 results: Redshift calibration of the MagLim++ lens sample

In this work, we derive and calibrate the redshift distribution of the MagLim++ lens galaxy sample used in the Dark Energy Survey Year 6 (DES Y6) 3 x 2pt cosmology analysis. The 3 x 2pt analysis combines galaxy clustering from the lens galaxy sample and weak gravitational lensing. The redshift distributions are inferred using the SOMPZ method - a Self-Organizing Map framework that combines deep-field multi-band photometry, wide-field data, and a synthetic source injection ( B alrog) catalog. Key improvements over the DES Year 3 (Y3) calibration include a noise-weighted SOM metric, an expanded Balrog catalogue, and an improved scheme for propagating systematic uncertainties, which allows us to generate O(10 8 ) redshift realizations that collectively span the dominant sources of uncertainty. These realizations are then combined with independent clustering-redshift measurements via importance sampling. The resulting calibration achieves typical uncertainties on the mean redshift of 1-2%, corresponding to a 20-30% average reduction relative to DES Y3. We compress the n(z) uncertainties into a small number of orthogonal modes for use in cosmological inference. Marginalizing over these modes leads to only a minor degradation in cosmological constraints. Here, this analysis establishes the MagLim++ sample as a robust lens sample for precision cosmology with DES Y6 and provides a scalable framework for future surveys.

dark energy↗

Discovery of spontaneous mesoscopic strain waves in nematic domains using dark-field x-ray microscopy

Electronic nematic order arises when correlated electrons spontaneously break the rotational symmetry of a crystal lattice. When electronic nematic order couples bilinearly to symmetry-breaking lattice strain, both appear together at a single ferroelastic phase transition, producing structural twin domains with distinct orientations of the nematic director. While the effects of applied strain on these domains are well established, the intrinsic behavior of spontaneous subdomain strain fields has remained unexplored. Here, we report the discovery of spontaneous mesoscopic strain waves within individual nematic domains of an iron-based superconductor, observed using dark-field x-ray microscopy (DFXM). Using this advanced full-field imaging technique, we visualize subdomain strain modulations emerging concurrently with nematic order. Elastic compatibility relations governing inhomogeneous strains provide a natural mechanism for the strain waves. Our findings reveal a broadly relevant form of strain self-organization and position DFXM as a powerful probe of the local interplay between lattice strain and electronic order.

36 MATERIALS SCIENCE↗

Investigation of design principles for metal-binding and conductive protein assemblies

Throughout the lifetime of this initiative, including renewals, we focused on understanding the fundamental principles of protein-protein interface design that enable predictable and modular spatial and kinetic control of multi-component protein self-assembly in 1D, 2D, and 3D, including the interface with inorganic materials, small molecules, and metal ions. We designed individual protein components that bind specific metal ions, including REEs and transport ions across lipid membranes. We created helical 1D filaments of repeating units with programmed periodicity, pitch, and multi-component environmentally responsive self-assembling protein fibers. We showed that these filaments reversibly assemble and disassemble under specific pH conditions and created end-specific caps that independently tune the balance of attachment and detachment rates at each terminus of the filament. Using similar filaments, we succeeded in binding arrays of heme and chlorophyll molecules and assembling patterned helical coatings around carbon nanotubes in efforts to create de novo conductive nanowires. By arraying REE binding sites in a large circular tandem array with a repeat protein-based cyclic oligomer, we created a molecular scaffold for superradiance and paramagnetic quantum sensing. We created a range of one-component and two-component self-assembling 2D arrays and showed that when designed to engage cell receptors, these arrays can control cell behavior from outside the cell signal to inside the cell. We designed helical repeat proteins with variable lengths displaying charged residues in a pattern matched to the cation lattice of mica. achieved a range of ordered states with an epitaxial match to the underlying crystal lattice. We further applied the learned principles of protein-induced biomineralization to design proteins with an interface lattice matching CaCO 3 and guide the formation of specific crystal forms of CaCO 3 from solution, a significant advance toward the global need to manage carbon. In all cases of mineral lattice matching and biomineralization, we followed assembly using molecularly resolved in situ AFM imaging and extracted information about assembly pathways and energetics, applying deep learning to quantify the dynamics of protein self-organization. We developed techniques for using dynamic metal-dependent interfaces on protein nanopores for discriminatively sensing dilute REEs in solution and demonstrated the use of strong metal-binding interfaces to drive nanocage disassembly for conditional nanocompartmentalization applications. This grant supported 11 people, including Asim Bera, Evans Brackenbrough, Andrew Borst, Nikita Hanikel, Timothy Huddy, Emily Joyce, Alex Young-Seug Kang, Ryan Kibler, Joshua Morris Lubner, Harley Pyles, and Shuai Zhang. The research effort culminated in the production of published papers and theses. Electronic Thesis/Dissertation are distributed by ProQuest/UMI Dissertation Publishing and made available on an open access basis through UW Libraries ResearchWorks Service.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Regime Characterization of Offshore Wind Resource Using Unsupervised Learning

Predictability of wind resource conditions is critical for offshore wind design and operations. While many studies of extreme wind conditions focus on specific events such as low-level jets or ramps, these rely on threshold definitions that limit generality. Here we present a data-driven framework that combines principal component analysis (PCA), self-organizing maps (SOM), and k-means clustering to classify wind resource conditions as typical and anomalous from climatological data. Anomalies are defined not by fixed thresholds but by flagging samples located far from SOM node centers inside the baseline SOM structure. This reframes extremes as rare ebents and hence, likely difficult to anticipate by numerical weather prediction models. We applied this approach to 23 years (2000–2022) of hourly profiles from the NOW-23 hindcast model at the Humboldt Wind Energy Area. Classification is conducted on a feature space consisting of 10 m wind speed and direction, bulk shear and veer across 30–270 m, and a low-level jet index. Dimensionality reduction is achieved through PC. A 2 × 3 OM lattice trained on the PCA vectors identified six baseline regimes spanning weak to strong flow states. High quantization-error profiles are identified and re-clustered into four anomalous regimes. The baseline regimes exhibited clear seasonal and diurnal cycles. Meanwhile, the anomalous regimes represented <10 % of all hours but showed distinct combinations of speed, shear, and veer, when compared to the baseline regimes. Anomalous regimes are typically short-lived (~few hours), yet their transitions can lead to hub-height wind changes of −18 to +9 m s -1 . For a representative 15 MW turbine, these shifts imply rapid swings in capacity factor from near-full output to negligible generation. Validation with lidar buoy data showed 51% agreement in SOM labels across ~6,000 overlapping hours, with most mismatches confined to adjacent speed classes. HRRR comparisons further revealed that anomalous regimes were disproportionately associated with forecast biases exceeding 5 m s -1 . Together, these results reframe extremes in offshore wind from absolute maxima or minima to weather states that are difficult to anticipate from models.

17 WIND ENERGY↗

Mesoscale Organization in Cumulus-Coupled Stratocumulus

Marine cloud systems cover a substantial portion of the world’s oceans. Most of these clouds form relatively close to the ocean surface, typically within one to two kilometers, a region referred to by meteorologists as the marine boundary layer. They are composed predominantly of liquid water, although ice particles can occur in mid- and high-latitude marine clouds during winter. In satellite imagery, these clouds appear bright against the darker ocean surface below, reflecting a large fraction of incoming sunlight back into space that would otherwise warm the ocean. Because marine boundary layer clouds cover such an extensive area of the ocean, they exert a significant influence on Earth’s overall transfer of solar energy absorbed by the surface and thermal energy emitted to space, a balance known as the planetary radiation budget. Marine boundary layer clouds are typically thin, and their formation and dissipation depend on a delicate balance between processes acting at the ocean surface below and the warm, dry air above. They are notoriously difficult to simulate accurately in weather forecast models, which often produce too few marine low clouds in midlatitudes and clouds in tropical regions that are excessively bright, meaning they reflect too much solar radiation. The marine boundary layer is frequently characterized by widespread overcast cloud cover that often transitions from a continuous, single-layer deck to more broken cloud fields toward the tropics. These transitions typically proceed through an intermediate stage in which shallow, broken clouds form beneath the overlying stratiform cloud deck. Once broken clouds develop below the overcast, they frequently self-organize into cloud clusters known as marine boundary layer convective complexes (MBLCCs), although the mechanisms governing the formation and organization of MBLCCs remain poorly understood. Accurately representing these transitions in long-range weather forecast models is essential because they influence the properties of air masses advected over the continental United States and Europe, and they become increasingly important for forecasts on seasonal and longer timescales. We employed two complementary approaches to investigate the processes controlling MBLCCs and their impact on marine cloud cover. Long-term observations from the U.S. Department of Energy’s Eastern North Atlantic (ENA) Observatory provided a unique dataset that allowed us to characterize fundamental properties of MBLCCs, including their typical size and frequency of occurrence. These observations were combined with high-resolution numerical simulations performed on supercomputers to examine the evolution of MBLCCs during cold-air outbreaks over the ENA region.

54 ENVIRONMENTAL SCIENCES↗

Stakeholder-guided holistic, Adaptive Framework for enhancing community Energy Resilience (SAFER) (Final Technical Report)

The Stakeholder-guided holistic, Adaptive Framework for enhancing community Energy Resilience (SAFER) project advances resilience science and engineering by addressing challenges in rural Kansas communities where aging infrastructure, extreme weather, and socioeconomic disparities heighten vulnerability to energy disruptions. Traditional approaches often focus on technical performance while overlooking community concerns and priorities. SAFER responds by integrating community perspectives with advanced analytical frameworks to create a holistic model for measuring and improving resilience. Project objectives included developing novel resilience metrics, advancing modeling frameworks that capture interdependencies across infrastructures, and embedding community-centric indicators directly into planning processes for distributed energy resources. The key technical innovations included the creation of self-organizing map (SOM)-based indices for objective resilience quantification, hetero-functional graph theory (HFGT) models linking power, water, transportation, and community assets, and graph neural network (GNN) tools for identifying critical nodes in complex systems. Community-centric energy planning was demonstrated through optimal siting and sizing of (photovoltaic) PV and battery storage, ensuring resilience enhancements also addressed energy burden and energy insecurity. SAFER engaged community partners in Dodge City and Ford County through surveys, focus groups, and workshops, generating more than 600 responses that established baseline measures of energy burden, financial insecurity, and willingness-to-pay to avoid outages. This data, organized in terms of a community capitals framework, informed the development of weighted reliability indices that better reflect community costs than traditional utility metrics. SAFER’s GNN-based critical node identification framework identified expert-labelled critical nodes with over 99% accuracy, while also uncovering additional functionalities essential for proactive resilience planning. The project’s models demonstrated that optimal PV and storage deployment could improve resilience indices by over 11 percent, with dispatch strategies further enhancing outcomes, confirming both the technical effectiveness and economic feasibility of these approaches. Through its combined emphasis on rigorous modeling, community-focused planning, and community engagement, SAFER advances the state of resilience research while delivering direct benefits to rural communities. The project provides tools, guidelines, and resilience heatmaps that help utilities, local governments, and residents better anticipate disruptions, prioritize investments, and strengthen the capacity to withstand and recover from energy-related hazards. Furthermore, the developed HFG and GNN frameworks are designed for transferability, allowing them to be adapted for resilience planning in other communities with minimal retraining. This inductive learning capability provides a scalable pathway to extend the SAFER project’s impact. Thus, creating a foundation for a nationally applicable model of infrastructure resilience. Additionally, the HFG can also be extended to include other FEMA community lifelines.

14 SOLAR ENERGY↗

The DECADE cosmic shear project II: photometric redshift calibration of the source galaxy sample

We present the photometric redshift characterization and calibration for the Dark Energy Camera All Data Everywhere (DECADE) weak lensing dataset: a catalog of 107 million galaxies observed by the Dark Energy Camera (DECam) in the northern Galactic cap. The redshifts are estimated from a combination of wide-field photometry, deep-field photometry with associated redshift estimates, and a transfer function between the wide field and deep field that is estimated using a source injection catalog. We construct four tomographic bins for the galaxy catalog, and estimate the redshift distribution, $n(z)$, within each one using the Self-organizing Map Photo-Z (SOMPZ) methodology. Our estimates include the contributions from sample variance, zeropoint calibration uncertainties, and redshift biases, as quantified for the deep-field dataset. The total uncertainties on the mean redshifts are $σ_{\langle}$$_z$$_{\rangle} ≈ 0.01$. The SOMPZ estimates are then compared to those from the clustering redshift method, obtained by cross-correlating our source galaxies with galaxies in spectroscopic surveys, and are shown to be consistent with each other.

Anbajagane, D. [Univ. of Chicago, IL (United State↗

A Unified Photometric Redshift Calibration for Weak Lensing Surveys Using the Dark Energy Spectroscopic Instrument

The effective redshift distribution n(z) of galaxies is a critical component in the study of weak gravitational lensing. Here, we introduce a new method for determining n(z) for weak lensing surveys based on high-quality redshifts and neural-network-based importance weights. Additionally, we present the first unified photometric redshift calibration of the three leading stage-III weak lensing surveys, the Dark Energy Survey (DES), the Hyper Suprime-Cam (HSC) survey, and the Kilo-Degree Survey (KiDS), with state-of-the-art spectroscopic data from the Dark Energy Spectroscopic Instrument (DESI). We verify our method using a new, data-driven approach and obtain n(z) constraints with statistical uncertainties of the order of $σ_z$ ~ 0.01 and smaller. Our analysis is largely independent of previous photometric redshift calibrations and, thus, provides an important cross-check in light of recent cosmological tensions. Overall, we find excellent agreement with previously published results on the DES Y3 and HSC Y1 data sets, while there are some differences on the mean redshift with respect to the previously published KiDS-1000 results. We attribute the latter to mismatches in photometric noise properties in the COSMOS field compared to the wider KiDS self-organizing map-gold catalog. At the same time, the new n(z) estimates for KiDS do not significantly change estimates of cosmic structure growth from cosmic shear. Finally, we discuss how our method can be applied to future weak lensing calibrations with DESI data.

Lange, J. U. [American Univ., Washington, DC (Unit↗

Synoptic Weather Regime Classifications for June, July and August, from 2000 to 2025

The synoptic weather regime classification has become a highly demanded product for the ARM site in recent years. This type of regime classification has shown applications in various studies and topics, including aerosol-cloud interactions, land-atmosphere interactions, and cloud radiative effects. The VAP employs an unsupervised machine learning method, Self-organizing map (SOM), to classify weather regimes for each day of the AMF campaigns and fixed sites, using ERA5 data. This idea is mainly based on our published study for TRACER in Wang et al. (2022, JGR-A).

node_som_ml↗

Synoptic Weather Regime Classifications for December, January and February, from 2000 to 2025

The synoptic weather regime classification has become a highly demanded product for the ARM site in recent years. This type of regime classification has shown applications in various studies and topics, including aerosol-cloud interactions, land-atmosphere interactions, and cloud radiative effects. The VAP employs an unsupervised machine learning method, Self-organizing map (SOM), to classify weather regimes for each day of the AMF campaigns and fixed sites, using ERA5 data. This idea is mainly based on our published study for TRACER in Wang et al. (2022, JGR-A).

{node_som_ml,synop_wea_reg}↗

Synoptic Weather Regime Classifications for September, October and November, from 2000 to 2025

The synoptic weather regime classification has become a highly demanded product for the ARM site in recent years. This type of regime classification has shown applications in various studies and topics, including aerosol-cloud interactions, land-atmosphere interactions, and cloud radiative effects. The VAP employs an unsupervised machine learning method, Self-organizing map (SOM), to classify weather regimes for each day of the AMF campaigns and fixed sites, using ERA5 data. This idea is mainly based on our published study for TRACER in Wang et al. (2022, JGR-A).

node_som_ml↗

Dark Energy Survey Year 6 Results: Redshift Calibration of the MagLim++ Lens Sample

In this work, we derive and calibrate the redshift distribution of the MagLim++ lens galaxy sample used in the Dark Energy Survey Year 6 (DES Y6) 3x2pt cosmology analysis. The 3x2pt analysis combines galaxy clustering from the lens galaxy sample and weak gravitational lensing. The redshift distributions are inferred using the SOMPZ method - a Self-Organizing Map framework that combines deep-field multi-band photometry, wide-field data, and a synthetic source injection (Balrog) catalog. Key improvements over the DES Year 3 (Y3) calibration include a noise-weighted SOM metric, an expanded Balrog catalogue, and an improved scheme for propagating systematic uncertainties, which allows us to generate O($10^8$) redshift realizations that collectively span the dominant sources of uncertainty. These realizations are then combined with independent clustering-redshift measurements via importance sampling. The resulting calibration achieves typical uncertainties on the mean redshift of 1-2%, corresponding to a 20-30% average reduction relative to DES Y3. We compress the $n(z)$ uncertainties into a small number of orthogonal modes for use in cosmological inference. Marginalizing over these modes leads to only a minor degradation in cosmological constraints. This analysis establishes the MagLim++ sample as a robust lens sample for precision cosmology with DES Y6 and provides a scalable framework for future surveys.

Giannini, G. [Chicago U., Astron. Astrophys. Ctr.;↗

Dark Energy Survey Year 6 Results: Redshift Calibration of the Weak Lensing Source Galaxies

Determining the distribution of redshifts for galaxies in wide-field photometric surveys is essential for robust cosmological studies of weak gravitational lensing. We present the methodology, calibrated redshift distributions, and uncertainties of the final Dark Energy Survey Year 6 (Y6) weak lensing galaxy data, divided into four redshift bins centered at $\langle z \rangle = [0.414, 0.538, 0.846, 1.157]$. We combine independent information from two methods on the full shape of redshift distributions: optical and near-infrared photometry within an improved Self-Organizing Map $p(z)$ (SOMPZ) framework, and cross-correlations with spectroscopic galaxy clustering measurements (WZ), which we demonstrate to be consistent both in terms of the redshift calibration itself and in terms of resulting cosmological constraints within 0.1$σ$. We describe the process used to produce an ensemble of redshift distributions that account for several known sources of uncertainty. Among these, imperfection in the calibration sample due to the lack of faint, representative spectra is the dominant factor. The final uncertainty on mean redshift in each bin is $σ_{\langle z\rangle} = [0.012, 0.008,0.009, 0.024]$. We ensure the robustness of the redshift distributions by leveraging new image simulations and a cross-check with galaxy shape information via the shear ratio (SR) method.

Yin, B. [Duke U.] (ORCID:0009000656049980)↗

The Power of DESI for Photometric Redshift Calibration: A Case Study with KiDS-1000

Accurate redshift estimates are a critical requirement for weak lensing surveys and one of the main uncertainties in constraints on dark energy and large-scale cosmic structure. In this paper, we study the potential to calibrate photometric redshift (photo-z) distributions for gravitational lensing using the Dark Energy Spectroscopic Instrument (DESI). Since beginning its science operations in 2021, DESI has collected more than 50 million redshifts, adding about one million monthly. In addition to its large-scale structure samples, DESI has also acquired over 256k high-quality spectroscopic redshifts (spec-zs) in the COSMOS and XMM and VVDS fields. This is already a factor of 3 larger than previous spec-z calibration compilations in these two regions. Here, we explore calibrating photo-zs for the subset of KiDS-1000 galaxies that fall into joint self-organizing map (SOM) cells overlapping the DESI COSMOS footprint using the DESI COSMOS observations. Estimating the redshift distribution in KiDS-1000 with the new DESI data, we find broad consistency with previously published results while also detecting differences in the mean redshift in some tomographic bins with an average shifts of Delta Mean(z) = -0.028 in the mean and Delta Median(z) = +0.011 in the median across tomographic bins. However, we also find that incompleteness per SOM cell, i.e., groups of galaxies with similar colors and magnitudes, can modify n(z) distributions. Finally, we comment on the fact that larger photometric catalogs, aligned with the DESI COSMOS and DESI XMM and VVDS footprints, would be needed to fully exploit the DESI dataset and would extend the coverage to nearly eight times the area of existing 9-band photometry.

Blanco, Diana [UC, Santa Cruz; UC, Santa Cruz, Ins↗

Microscopic Imprints of Learned Solutions in Tunable Networks

In physical networks trained using supervised learning, physical parameters are adjusted to produce desired responses to inputs. An example is an electrical contrastive local learning network of nodes connected by edges that adjust their conductances during training. When an edge conductance changes, it upsets the current balance of every node. In response, physics adjusts the node voltages to minimize the dissipated power. Learning in these systems is therefore a coupled double-optimization process, in which the network descends both a cost landscape in the high-dimensional space of edge conductances and a physical landscape—the power dissipation—in the high-dimensional space of node voltages. Because of this coupling, the physical landscape of a trained network contains information about the learned task. Here, we derive a structure-function relation for trained tunable networks and demonstrate that all the physical information relevant to the trained input-output relation can be captured by a tuning susceptibility, an experimentally measurable quantity. We supplement our theoretical results with simulations to show that the tuning susceptibility is correlated with functional importance and that we can extract physical insight into how the system performs the task from the conductances of highly susceptible edges. Our analysis is general and can be applied directly to mechanical networks, such as networks trained for protein-inspired function such as allostery.

36 MATERIALS SCIENCE↗