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DOE OSTI2024

Quantifying structural errors in cloud condensation nuclei activity from reduced representation of aerosol size distributions

Aerosol effects on clouds and radiation are the dominant contribution to uncertainty in radiative forcing relative to the pre-industrial atmosphere. While previous studies have assessed the impact of parametric uncertainty on modeled forcing, structural errors from the numerical representation of particle distributions have not been well quantified. Here we present a framework for quantifying error in aerosol size distributions and cloud condensation nuclei activity, which we apply to the widely used 4-mode version of the Modal Aerosol Module (MAM4). Box model predictions from the MAM4 are evaluated against the Particle Monte Carlo Model for Simulating Aerosol Interactions and Chemistry (PartMC-MOSAIC), a benchmark model that tracks the evolution of individual particles. We show that size distributions simulated by MAM4 diverge from those simulated by PartMC-MOSAIC after only a few hours of aging by condensation and coagulation in polluted conditions, which leads to large errors in modeled cloud condensation nuclei concentrations. We find that differences between MAM4 and PartMC-MOSAIC are largest under polluted conditions, where the size distribution evolves rapidly though aging by condensation of semi-volatile substances and coagulation among particles. These findings suggest that structural error in modeled aerosol properties contributes to the large inter-model variability in aerosol radiative forcing.

Fierce, Laura M.↗

DOE OSTI2025

Two deeply conserved non-coding sequences control PLETHORA1/2 expression and coordinate embryo and root development

Conserved non-coding sequences (CNSs) are integral elements of transcriptional regulation. Transcriptional tuning of PLETHORA (PLT) genes that encode master regulators of plant development is vital for embryogenesis and meristematic function. However, how the expression of PLT genes is modulated through CNSs remains unclear. Through motif-based mining of upstream sequences in 120 angiosperm genomes, we identified 21 conserved and lineage-specific CNSs, two of which are unusually long, similar, and colinear within eudicots. Using Arabidopsis thaliana, we demonstrate that these two deeply conserved elements, which we named BOX1 and BOX2, control PLT1 and PLT2 expression. CRISPR mutants within these elements specifically reduced PLT expression levels, and reporter lines revealed that deletion of either or both BOXes altered and/or abrogated the PLT2 expression pattern in the root tip, affecting the ability to rescue the plt1 plt2 double mutant. We further show that the influence of these elements on expression patterns is already exerted during embryogenesis and functional in the context of the early embryo. Finally, we reveal the existence of a BOX-mediated autoregulatory feedback loop that, in large part, explains CNS influence on expression patterns. We thus uncover a transcriptional mechanism by which genes encoding master regulators of embryo and root meristem development are regulated.

PLETHORA↗

DOE OSTI2024

RG-CAT: Detection pipeline and catalogue of radio galaxies in the EMU pilot survey

Abstract We present source detection and catalogue construction pipelines to build the first catalogue of radio galaxies from the 270$\rm deg^2$pilot survey of the Evolutionary Map of the Universe (EMU-PS) conducted with the Australian Square Kilometre Array Pathfinder (ASKAP) telescope. The detection pipeline uses Gal-DINO computer vision networks (Gupta et al. 2024, PASA, 41, e001) to predict the categories of radio morphology and bounding boxes for radio sources, as well as their potential infrared host positions. The Gal-DINO network is trained and evaluated on approximately 5 000 visually inspected radio galaxies and their infrared hosts, encompassing both compact and extended radio morphologies. We find that the Intersection over Union (IoU) for the predicted and ground-truth bounding boxes is larger than 0.5 for 99% of the radio sources, and 98% of predicted host positions are within$3^{\prime \prime}$of the ground-truth infrared host in the evaluation set. The catalogue construction pipeline uses the predictions of the trained network on the radio and infrared image cutouts based on the catalogue of radio components identified using theSelavysource finder algorithm. Confidence scores of the predictions are then used to prioritiseSelavycomponents with higher scores and incorporate them first into the catalogue. This results in identifications for a total of 211 625 radio sources, with 201 211 classified as compact and unresolved. The remaining 10 414 are categorised as extended radio morphologies, including 582 FR-I, 5 602 FR-II, 1 494 FR-x (uncertain whether FR-I or FR-II), 2 375 R (single-peak resolved) radio galaxies, and 361 with peculiar and other rare morphologies. Each source in the catalogue includes a confidence score. We cross-match the radio sources in the catalogue with the infrared and optical catalogues, finding infrared cross-matches for 73% and photometric redshifts for 36% of the radio galaxies. The EMU-PS catalogue and the detection pipelines presented here will be used towards constructing catalogues for the main EMU survey covering the full southern sky.

Astronomy & Astrophysics↗

DOE OSTI2024

Removing Basis Set Incompleteness Error in Finite-Temperature Electronic Structure Calculations: Two-Electron Systems

We investigate the basis-set-size dependence for quantities related to interacting electrons in the canonical ensemble. Calculations are performed using exact diagonalization (finite temperature full configuration interaction method) on two-electron model systems–the uniform electron gas (UEG) and the helium atom. Our data reproduce previous observations of a competition for how the internal energy converges between the ground-state correlation energy and the high-temperature kinetic energy. We explore how this can be related to component parts of the internal energy including kinetic, exchange, and correlation energies and show there is surprising nuance in how this can be broken down into mostly monotonically converging quantities. We also show that separation of the free energy into a free energy with/without correlation allows for monotonic convergence with basis set size due to the variational principle. We find that the free energy convergence matches the previously observed convergence properties of the internal energy. We discuss the free energy divergence that happens when converging a finite basis analytical hydrogen atom to the complete basis set limit and compare this to the energies of a helium atom in a large periodic box. Reducing the box size, we saw convergence trends for the helium atom that were similar to the UEG.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Structure of Novel Phosphonium-Based Ionic Liquids with S and O Substitutions from Experiments and a Mixed Quantum-Classical Approach

This article presents experimental characterization information and synchrotron X-ray scattering measurements on a set of novel O- and S-substituted phosphonium-based ionic liquids (ILs) all coupled with the bis(fluorosulfonyl)imide (FSI-) anion. The ILs include the ethoxyethyltriethylphosphonium (P 222(2O2) + ) and triethyl[2-(ethylthio)ethyl]phosphonium (P 222(2S2) + ) cations, and we contrast results on these with those for unsubstituted triethylpentylphosphonium (P 2225 + ). The article also introduces a physics-based protocol that combines classical force field studies on larger simulation boxes with classical and first-principles studies on smaller boxes. The method produces significantly improved S(q) functions in the regime which in prior publications we have associated with inter- and intraionic adjacency correlations. By understanding which shorter-range structural changes improve S(q) in the q-regime of interest, we are also able to pinpoint specific deficiencies in the classical force field model. The approach we take should be quite general and could help study other complex liquids on different length scales.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Cryo-EM structures of the small-conductance Ca 2+ -activated K Ca 2.2 channel

Small-conductance Ca 2+ -activated K + (K Ca 2.1-K Ca 2.3) channels modulate neuronal and cardiac excitability. We report cryo-electron microscopy structures of the K Ca 2.2 channel in complex with calmodulin and Ca 2+ , alone or bound to two small molecule inhibitors, at 3.18, 3.50, 2.99 and 2.97 angstrom resolution, respectively. Extracellular S3-S4 loops in β-hairpin configuration form an outer canopy over the pore with an aromatic box at the canopy’s center. Each S3-S4 β-hairpin is tethered to the selectivity filter in the neighboring subunit by inter-subunit hydrogen bonds. This hydrogen bond network flips the aromatic residue (Tyr362) in the filter’s GYG signature by 180°, causing the outer selectivity filter to widen and water to enter the filter. Disruption of the tether by a mutation narrows the outer selectivity filter, realigns Tyr362 to the position seen in other K + channels, and significantly increases unitary conductance. UCL1684, a mimetic of the bee venom peptide apamin, sits atop the canopy and occludes the opening in the aromatic box. AP14145, an analogue of a therapeutic for atrial fibrillation, binds in the central cavity below the selectivity filter and induces closure of the inner gate. These structures provide a basis for understanding the small unitary conductance and pharmacology of K Ca 2.x channels.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

A physics informed bayesian optimization approach for material design: application to NiTi shape memory alloys

Abstract The design of materials and identification of optimal processing parameters constitute a complex and challenging task, necessitating efficient utilization of available data. Bayesian Optimization (BO) has gained popularity in materials design due to its ability to work with minimal data. However, many BO-based frameworks predominantly rely on statistical information, in the form of input-output data, and assume black-box objective functions. In practice, designers often possess knowledge of the underlying physical laws governing a material system, rendering the objective function not entirely black-box, as some information is partially observable. In this study, we propose a physics-informed BO approach that integrates physics-infused kernels to effectively leverage both statistical and physical information in the decision-making process. We demonstrate that this method significantly improves decision-making efficiency and enables more data-efficient BO. The applicability of this approach is showcased through the design of NiTi shape memory alloys, where the optimal processing parameters are identified to maximize the transformation temperature.

Chemistry↗

DOE OSTI2025

Enhancing generative molecular design via uncertainty-guided fine-tuning of variational autoencoders

In recent years, deep generative models have been successfully applied to various molecular design tasks, particularly in the life and materials sciences. One critical challenge for pre-trained generative molecular design (GMD) models is to fine-tune them to be better suited for downstream design tasks that aim at optimizing specific molecular properties. However, redesigning and training an existing effective generative model from scratch for each new design task are impractical. Furthermore, the black-box nature of typical downstream tasks that involve property prediction makes it nontrivial to optimize the generative model in a task-specific manner. In this work, we propose an uncertainty-guided fine-tuning strategy that can effectively enhance a pre-trained variational autoencoder (VAE) for GMD through performance feedback in an active learning setting. The strategy begins by quantifying the model uncertainty of the generative model using an efficient active subspace-based UQ (uncertainty quantification) scheme. Next, the decoder diversity within the characterized model uncertainty class is explored to expand the viable space of molecular generation. The low-dimensionality of the active subspace makes this exploration tractable using a black-box optimization scheme, which in turn enables us to identify and leverage a diverse set of high-performing models to generate enhanced molecules. Empirical results across six target molecular properties using multiple VAE-based generative models demonstrate that our uncertainty-guided fine-tuning strategy consistently leads to improved models that outperform the original pre-trained models.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Improving the precision of forces in real-space pseudopotential density functional theory

The high-order finite difference real-space pseudopotential density functional theory (DFT) approach is a valuable method for large-scale, massively parallel DFT calculations. A significant challenge in the approach is the oscillating “egg-box” error introduced by aliasing associated with a coarse grid spacing. To address this issue while minimizing computational cost, we developed a finite difference interpolation (FDI) scheme [Roller et al., J. Chem. Theory Comput. 19, 3889 (2023)] as a means of exploiting the high resolution of the pseudopotential to reduce egg-box effects systematically. Here, we show an implementation of this method in the PARSEC code and examine the practical utility of the combination of FDI with additional methods for improving force precision and/or reducing its computational cost, including orbital-based forces, compensating charges (namely, adding and subtracting a judiciously chosen charge density such that the total density is unaltered), and a modified spatial domain in which the real-space grid is defined. Using selected small molecules, as well as metallic Li, as test cases, we show that a combination of all four aspects leads to a significant reduction in computational cost while retaining a high level of precision that supports accurate structures and vibrational spectra, as well as stable and accurate molecular dynamics runs.

Chemistry↗

DOE OSTI2026

Degenerate coupled-cluster theory

A size-extensive, converging, black-box, ab initio coupled-cluster (ΔCC) ansatz is introduced that computes the energies and wave functions of states from any degenerate or nondegenerate Slater-determinant references with any numbers of α- and β-spin electrons, any patterns of orbital occupancy, any spin multiplicities, and any spatial symmetries. For a nondegenerate reference, it reduces to the single-reference coupled-cluster ansatz. For a degenerate multireference, it is a natural coupled-cluster extension of degenerate Møller–Plesset perturbation (ΔMP) theory. For ionized and electron-attached references, it is a coupled-cluster Green’s function, although the present theory is convergent toward the full-configuration-interaction limits, while the Feynman–Dyson many-body Green’s function (MBGF) theory generally is not. Its single-excitation instance is a projection Hartree–Fock theory as per the Thouless theorem, which may be useful for core ionizations, high-spin states, and possibly electron affinities. Additionally, a new multireference coupled-cluster theory for a general model space is developed. This quasidegenerate coupled-cluster (QCC) theory is exactly converging, but not black-box, and intended for strong correlation. Determinant-based, general-order algorithms of ΔCC and QCC theories are implemented and compared with configuration-interaction (CI) and equation-of-motion coupled-cluster (EOM-CC) theories through octuple excitations and with ΔMP and MBGF theories up to the nineteenth order. An algebraic, optimal-scaling algorithm of the ΔCC theory is computer-synthesized at the levels of single excitations (ΔCCS) and of single and double excitations (ΔCCSD). As a result, the order of performance is QCC ≈ ΔCC > EOM-CC > CI at the same order or QCC ≈ ΔCC > ΔMP > MBGF at the same cost scaling.

Hirata, So [University of Illinois at Urbana-Champ↗

DOE OSTI2025

The GRAS protein RAM1 interacts with WRI transcription factors to regulate plant genes required for arbuscule development and function

During arbuscular mycorrhiza (AM) symbiosis AM fungi form tree-shaped structures called arbuscules in root cortex cells of host plants. Arbuscules and their host cells are central for reciprocal nutrient exchange between the symbionts.REQUIRED FOR ARBUSCULAR MYCORRHIZATION1(RAM1) encodes a GRAS protein crucial for transcriptionally regulating plant genes needed for arbuscule development and nutrient exchange. Similar to other GRAS proteins, RAM1 likely does not bind to DNA and how RAM1 activates its target promoters remained elusive. Here, we demonstrate that RAM1 interacts with five AM-induced APETALA 2 (AP2) transcription factors of the WRINKLED1-like family called CTTC MOTIF-BINDING TRANSCRIPTION FACTOR1 (CBX1), WRI3, WRI5a, WRI5b, and WRI5c via a C-terminal domain containing the M2/M2a motif. This motif is conserved and enriched in WRI proteins encoded by genomes of AM-competent plants. RAM1 together with any of these WRI proteins activates the promoters of genes required for symbiotic nutrient exchange, namelyRAM2,STUNTED ARBUSCULES (STR),andPHOSPHATE TRANSPORTER 4 (PT4), inNicotiana benthamianaleaves. This activation as well as target promoter induction inLotus japonicushairy roots depends onMYCS(MYCORRHIZA SEQUENCE)-elements andAW-boxes, previously identified as WRI-binding sites. TheWRIgenes are activated in two waves: Transcription ofRAM1,CBX1,andWRI3is coregulated by calcium- and calmodulin-dependent protein kinase-activated CYCLOPS, through theAMCYC-REin their promoter, and DELLA, whileWRI5a,b,andcpromoters containMYCS-elements andAW-boxes and can be activated by RAM1 heterocomplexes with CBX1 or WRI3. We propose that RAM1 provides an activation domain to DNA-binding WRI proteins to activate genes with central roles in AM development and function.

Science & Technology - Other Topics↗

DOE OSTI2025

Criticality analysis of nuclear binding energy neural networks

Machine learning methods, in particular deep learning methods such as artificial neural networks (ANNs) with many layers, have become widespread and useful tools in nuclear physics. However, these ANNs are typically treated as ‘black boxes’, with their architecture (width, depth, and weight/bias initialization) and the training algorithm and parameters chosen empirically by optimizing learning based on limited exploration. We test a non-empirical approach to understanding and optimizing nuclear physics ANNs by adapting a criticality analysis based on renormalization group flows in terms of the hyperparameters for weight/bias initialization, training rates, and the ratio of depth to width. This treatment utilizes the statistical properties of neural network initialization to find a generating functional for network outputs at any layer, allowing for a path integral formulation of the ANN outputs as a Euclidean statistical field theory. We use a prototypical example to test the applicability of this approach: a simple ANN for nuclear binding energies. We find that with training using a stochastic gradient descent optimizer, the predicted criticality behavior is realized, and optimal performance is found with critical tuning. However, the use of an adaptive learning algorithm leads to somewhat superior results without concern for tuning and thus obscures the analysis. Nevertheless, the criticality analysis offers a way to look within the black box of ANNs, which is a first step towards potential improvements in network performance beyond using adaptive optimizers.

artificial neural network↗

DOE OSTI2024

Cryogenic aspects of a 20 MW class low-temperature superconducting generator for the renewables industry

In this paper we give a progress update on the cryogenic design for cooling a 20 MW class, partially superconducting generator with stationary field coils for offshore wind renewables industry [1-2]. This is a continuation of an earlier program on a 10 MW system dating back ten years. Whereas this new power rating increase leads to a radial diameter expansion of the superconducting field coils from 4 to > 9.5 m, it maintains the axial length. We show the design based on this scaled up with enlarged diameter. The field coil size increase asks for higher cooling power that leads to a bigger cold box size to accommodate the cryocoolers. In the design, as many as 8 cryocoolers can be accessed and serviced from the nacelle that houses the main cryogenic components. A typical thermal load balance sheet with all components is given and compared against the available cryocooler cooling power at different operating conditions. Due to the cryocoolers’ local point of contact cooling within the nacelle, the temperature gradient of the thermal shield that fully encloses the cold mass with its embedded field coils needs to be balanced out to minimize the heat burden on the field coils. This requires additional analytical efforts and implementation of further design features. The extended nacelle houses the cold box with its cryogenic infrastructure. The interface for the envisaged cryogenic pushbutton closed-loop circulating system remains invisible, requires no handling of cryogenic liquids and is hermetically closed. The field coil diameter increase also leads to a greater initial helium gas storage volume. In addition, it requires higher initial room temperature fill pressure within the toroidal helium vapor storage tanks and in cooling tubes connecting to the cryocoolers. The toroidal helium gas tanks are thermally coupled with the thermal shield so that helium convection inside the storage tank can improve heat transfer and reduce the temperature gradient of the thermal shield. Besides those heat transfer challenges, additional mechanical strain within this large structure is exerted on the torque tubes during initial cooldown and when energizing field coils. Some of those design challenges are quite unexpected, leading to novel workarounds in order to maintain the chosen cooling strategy. Finally, we assess those design limitations in view of further cryogenic scalability with emphasis on manufacturability and assembly.

cryogenics↗

DOE OSTI2024

Generating mock galaxy catalogues for flux-limited samples like the DESI Bright Galaxy Survey

ABSTRACT Accurate mock galaxy catalogues are crucial to validate analysis pipelines used to constrain dark energy models. We present a fast HOD-fitting method which we apply to the AbacusSummit simulations to create a set of mock catalogues for the DESI Bright Galaxy Survey, which contain r-band magnitudes and $(g-r)$ colours. The halo tabulation method fits HODs for different absolute magnitude threshold samples simultaneously, preventing unphysical HOD crossing between samples. We validate the HOD fitting procedure by fitting to real-space clustering measurements and galaxy number densities from the MXXL BGS mock, which was tuned to the SDSS and GAMA surveys. The best-fitting clustering measurements and number densities are mostly within the assumed errors, but the clustering for the faint samples is low on large scales. The best-fitting HOD parameters are robust when fitting to simulations with different realizations of the initial conditions. When varying the cosmology, trends are seen as a function of each cosmological parameter. We use the best-fitting HOD parameters to create cubic box and cut sky mocks from the AbacusSummit simulations, in a range of cosmologies. As an illustration, we compare the ${}^{0.1}M_r\lt -20$ sample of galaxies in the mock with BGS measurements from the DESI one-percent survey. We find good agreement in the number densities, and the projected correlation function is reasonable, with differences that can be improved in the future by fitting directly to BGS clustering measurements. The cubic box and cut-sky mocks in different cosmologies are made publicly available.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Modest set of simulations of local-type primordial non-Gaussianity in the DESI era

A measurement of a primordial non-Gaussianity (PNG) signal through late- or early-Universe probes has the potential to transform our understanding of the physics of the primordial Universe. While large-scale structure observables in principle contain vital information, interpreting these measurements is challenging due to poorly understood astrophysical effects. Luckily, N-body simulations, such as the abacuspng set presented in this study, consisting of 9 boxes, each of size L box = 2 Gpc/h and particle mass of 1.01 × 10 10 M ⊙ /h, provide a viable path forward. As validation, we find good agreement between the simulations and our expectations from one-loop perturbation theory (PT) and the "separate universe" method for the matter bispectrum, matter power spectrum and the halo bias parameter associated with PNG, b φ . As a science application, here we investigate the link between halo assembly bias and b φ for halo properties known to play a vital role in accurately predicting galaxy clustering: concentration, shear (environment), and accretion rate. We find a strong response for all three parameters, suggesting that the connection between b φ and the assembly history of halos needs to be taken into account by future PNG analyses. We further perform the first study of the b φ parameter from fits to early DESI data of the luminous red galaxy (LRG) and quasistellar object (QSO) samples and comment on the effect on f NL constraints for the allowed galaxy-halo models (note that σ[f NL ]∝ $\frac{σ[b_φ]}{b_φ}$). We find that the error on f NL is 15, 8, 7 for the LRGs at z = 0.5 and z = 0.8 and QSOs at z = 1.4, respectively, suggesting that a thorough understanding of galaxy assembly bias is warranted so as to perform robust high-precision analysis of local-type PNG with future surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Grid Parameters and Voltage Estimation Approach Integrating Data-Driven Converter Model

With Measurements of grid voltage and current are essential for the optimal operation of the grid protection and control (P&C) systems. Grid parameters vary through time during the faults and especially in the converter interfaced resources (CIRs) rich power grid, and thus accurate estimation is critical to avoid the mis-operation of the P&C systems. In this paper, a moving horizon estimation (MHE) as an observer is devised and applied to estimate the grid line parameters and grid voltages for protection enhancement. Due to the proprietary and confidentiality of CIRs, the proposed approach uses the black-box model to represent their dynamics. Leveraging the easily accessible measurements of output current from the black-box model of CIR and voltage at the point of common coupling, the proposed method estimates the grid impedance and grid voltage during normal and faulty operating conditions. The performance shows that the optimization-based observer was able to closely observe the accurate states and parameters, which can be utilized by the P&C systems.

Subedi, Sunil↗

DOE OSTI2026

Optimal Methods for Estimating Cactus Pear Biomass Using Cladode Dimensions of Morphologically Diverse Accessions

Current allometric methods for photosynthetic-stem (cladode) plants, such as cactus pear (Opuntia spp.), require refinement to be used in field settings in which diverse accessions are grown. We analysed cladode dimensional data using 14 accessions representing four species and two hybrids to quantify statistically significant morphological differences among accessions and derived cross-accession models to approximate cladode fresh weight. A Box model using cladode dimensions (e.g., length, width, thickness and diameter) and factorial combinations of these measures (e.g., length*width*thickness*diameter vs. fresh weight) resulted in the highest coefficient of determination (R 2 = 0.95 general fit) across all accessions for estimating fresh weight along with parsimony estimates using the Schwarz–Bayes Criterion (SBC), which assesses the most consistent performance on individual accessions. A Fitting-box modelling approach used the measured cladode area captured using ImageJ (R 2 = 0.93 general fit). Lastly, an Elliptical model used an elliptical approximation for the measured area and performed well over all accessions (R 2 = 0.94 general fit) while avoiding extensive manual measurements. These models meet or exceed the performance of previously published approaches when applied across morphologically diverse accessions, providing efficient tools for nondestructive estimation of cactus pear biomass under the conditions tested.

Opuntia↗

DOE OSTI2024

Implementation and (Inverse Modified) Error Analysis for Implicitly Templated ODE-Nets

We focus on learning unknown dynamics from data using ODE-nets templated on implicit numerical initial value problem solvers. First, we perform inverse modified error analysis of the ODE-nets using unrolled implicit schemes for ease of interpretation. It is shown that training an ODE-net using an unrolled implicit scheme returns a close approximation of an inverse modified differential equation (IMDE). In addition, we establish a theoretical basis for hyperparameter selection when training such ODE-nets, whereas current strategies usually treat numerical integration of ODE-nets as a black box. We thus formulate an adaptive algorithm which monitors the level of error and adapts the number of (unrolled) implicit solution iterations during the training process, so that the error of the unrolled approximation is less than the current learning loss. This helps accelerate training while maintaining accuracy. Several numerical experiments are performed to demonstrate the advantages of the proposed algorithm compared to nonadaptive unrollings and validate the theoretical analysis. Here, we also note that this approach naturally allows for incorporating partially known physical terms in the equations, giving rise to what is termed “gray box” identification.

ODE-nets↗