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DOE OSTI2020

Electronic structure and photophysics of a supermolecular iron complex having a long MLCT-state lifetime and panchromatic absorption

Exploiting earth-abundant iron-based metal complexes as high-performance photosensitizers demands long-lived electronically excited metal-to-ligand charge-transfer (MLCT) states, but these species suffer typically from femtosecond timescale charge-transfer (CT)-state quenching by low-lying nonreactive metal-centered (MC) states. Here, we engineer supermolecular Fe(II) chromophores based on the bis(tridentate-ligand)metal(II)-ethyne-(porphinato)zinc(II) conjugated framework, previously shown to give rise to highly delocalized low-lying 3 MLCT states for other Group VIII metal (Ru, Os) complexes. Electronic spectral, potentiometric, and ultrafast pump–probe transient dynamical data demonstrate that a combination of a strong σ-donating tridentate ligand and a (porphinato)zinc(II) moiety with low-lying π*-energy levels, sufficiently destabilize MC states and stabilize supermolecular MLCT states to realize Fe(II) complexes that express 3 MLCT state photophysics reminiscent of their heavy-metal analogs. The resulting Fe(II) chromophore archetype, FeNHCPZn, features a highly polarized CT state having a profoundly extended 3MLCT lifetime (160 ps), 3 MLCT phosphorescence, and ambient environment stability. Density functional and domain-based local pair natural orbital coupled cluster [DLPNO-CCSD(T)] theory reveal triplet-state wavefunction spatial distributions consistent with electronic spectroscopic and excited-state dynamical data, further underscoring the dramatic Fe metal-to-extended ligand CT character of electronically excited FeNHCPZn. This design further prompts intense panchromatic absorptivity via redistributing high-energy absorptive oscillator strength throughout the visible spectral domain, while maintaining a substantial excited-state oxidation potential for wide-ranging photochemistry––highlighted by the ability of FeNHCPZn to photoinject charges into a SnO 2 /FTO electrode in a dye-sensitized solar cell (DSSC) architecture. Concepts enumerated herein afford opportunities for replacing traditional rare-metal–based emitters for solar-energy conversion and photoluminescence applications.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

Structure of pre-miR-31 reveals an active role in Dicer–TRBP complex processing

As an essential posttranscriptional regulator of gene expression, microRNA (miRNA) levels must be strictly maintained. The biogenesis of many miRNAs is mediated by trans-acting protein partners through a variety of mechanisms, including remodeling of the RNA structure. miR-31 functions as an oncogene in numerous cancers, and interestingly, its biogenesis is not known to be regulated by protein-binding partners. Therefore, the intrinsic structural properties of the precursor element of miR-31 (pre-miR-31) can provide a mechanism by which its biogenesis is regulated. We determined the solution structure of pre-miR-31 to investigate the role of distinct structural elements in regulating processing by the Dicer–TRBP complex. We found that the presence or absence of mismatches within the helical stem does not strongly influence Dicer–TRBP processing of the pre-miRNAs. However, both the apical loop size and structure at the Dicing site are key elements for discrimination by the Dicer–TRBP complex. Interestingly, our NMR-derived structure reveals the presence of a triplet of base pairs that link the Dicer cleavage site and the apical loop. Mutational analysis in this region suggests that the stability of the junction region strongly influences processing by the Dicer–TRBP complex. Our results enrich our understanding of the active role that RNA structure plays in regulating miRNA biogenesis, which has direct implications for the control of gene expression.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Viral afterlife: SARS-CoV-2 as a reservoir of immunomimetic peptides that reassemble into proinflammatory supramolecular complexes

It is unclear how severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection leads to the strong but ineffective inflammatory response that characterizes severe Coronavirus disease 2019 (COVID-19), with amplified immune activation in diverse cell types, including cells without angiotensin-converting enzyme 2 receptors necessary for infection. Proteolytic degradation of SARS-CoV-2 virions is a milestone in host viral clearance, but the impact of remnant viral peptide fragments from high viral loads is not known. Here, we examine the inflammatory capacity of fragmented viral components from the perspective of supramolecular self-organization in the infected host environment. Interestingly, a machine learning analysis to SARS-CoV-2 proteome reveals sequence motifs that mimic host antimicrobial peptides (xenoAMPs), especially highly cationic human cathelicidin LL-37 capable of augmenting inflammation. Such xenoAMPs are strongly enriched in SARS-CoV-2 relative to low-pathogenicity coronaviruses. Moreover, xenoAMPs from SARS-CoV-2 but not low-pathogenicity homologs assemble double-stranded RNA (dsRNA) into nanocrystalline complexes with lattice constants commensurate with the steric size of Toll-like receptor (TLR)-3 and therefore capable of multivalent binding. Such complexes amplify cytokine secretion in diverse uninfected cell types in culture (epithelial cells, endothelial cells, keratinocytes, monocytes, and macrophages), similar to cathelicidin’s role in rheumatoid arthritis and lupus. The induced transcriptome matches well with the global gene expression pattern in COVID-19, despite using <0.3% of the viral proteome. Delivery of these complexes to uninfected mice boosts plasma interleukin-6 and CXCL1 levels as observed in COVID-19 patients.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2023

Scientific machine learning for modeling and simulating complex fluids

The formulation of rheological constitutive equations—models that relate internal stresses and deformations in complex fluids—is a critical step in the engineering of systems involving soft materials. While data-driven models provide accessible alternatives to expensive first-principles models and less accurate empirical models in many engineering disciplines, the development of similar models for complex fluids has lagged. The diversity of techniques for characterizing non-Newtonian fluid dynamics creates a challenge for classical machine learning approaches, which require uniformly structured training data. Consequently, early machine-learning based constitutive equations have not been portable between different deformation protocols or mechanical observables. Here, we present a data-driven framework that resolves such issues, allowing rheologists to construct learnable models that incorporate essential physical information, while remaining agnostic to details regarding particular experimental protocols or flow kinematics. These scientific machine learning models incorporate a universal approximator within a materially objective tensorial constitutive framework. By construction, these models respect physical constraints, such as frame-invariance and tensor symmetry, required by continuum mechanics. We demonstrate that this framework facilitates the rapid discovery of accurate constitutive equations from limited data and that the learned models may be used to describe more kinematically complex flows. This inherent flexibility admits the application of these “digital fluid twins” to a range of material systems and engineering problems. We illustrate this flexibility by deploying a trained model within a multidimensional computational fluid dynamics simulation—a task that is not achievable using any previously developed data-driven rheological equation of state.

Science & Technology - Other Topics↗

DOE OSTI2025

An unusual Co–S bond links B 12 chaperones in an interprotein complex

Chaperones in trafficking pathways ensure specificity of transition metal loading and protection against adventitious side reactions. In B 12 , an essential cofactor for humans, a cobalt ion is coordinated to a >1.3 kDa tetrapyrrolic scaffold, posing logistical challenges for its translocation. In this study, we report the 3.4 Å crystal structure of the human MMACHC and MMADHC B 12 chaperones, tethered via a rarely seen covalent cobalt–sulfur bond. B 12 is bound in the base-off state to MMACHC, with Cys-261 on MMADHC serving as the upper axial ligand; the lower-axial position is vacant. The propensity of thiolato-cobalamin derivatives bound to MMACHC to undergo spontaneous decomposition via general acid catalysis or reduction/oxidation chemistry is averted in the interprotein complex with MMADHC. An exposed face in the complex suggests an exit route for B 12 . No known clinical variants localize to the interprotein interface, consistent with the cobalt–sulfur bond being key to forming the high-affinity complex.

Science & Technology - Other Topics↗

DOE OSTI2025

Action at a distance: The remarkable coupling of CO 2 uptake to electron transfer in specialized cyanobacterial NDH-1 complexes

Cyanobacteria achieve highly efficient photosynthesis using a CO 2 -concentrating mechanism relying on specialized Type I (NDH-1) complexes. Among these, NDH-1 3 and NDH-1 4 catalyze redox-coupled hydration of CO 2 to bicarbonate, supporting carbon fixation in carboxysomes. The mechanism of coupling electron transfer to CO 2 -hydration by these variant NDH-1 complexes remains unknown. We engineered a Synechococcus PCC7942 strain that expresses exclusively the high flux/low affinity NDH-14 complex, enabling the observation of the coupling of CO 2 hydration to cyclic electron flow in isolation from the other NDH-1 isoforms normally present in cells. We found that inhibition of the CupB protein by the carbonic anhydrase inhibitor ethoxzolamide (EZ) suppressed CO 2 uptake, slowed photosystem I rereduction, and abolished proton pumping as probed by acridine orange fluorescence. These effects were absent in strains lacking Cup proteins, confirming specificity. The results demonstrate that CO 2 hydration and electron transfer through NDH-14 are tightly coupled via proton translocation across the thylakoid membrane. These findings provide direct evidence for the bidirectional interaction in bioenergetic coupling between the plastoquinone reduction and the CO 2 uptake at the distal Zn-site over a span of ~150 Å and support a proton-removal hypothesis involving the proton transfer pathways from the Zn-site of CO2 hydration to an energetically coupled proton loading site evolutionarily repurposed from the ancestral proton pumping mechanism to enable energetic CO 2 uptake.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2017

Structural and biochemical analyses reveal insights into covalent flavinylation of the Escherichia coli Complex II homolog quinol:fumarate reductase

The Escherichia coli Complex II homolog quinol:fumarate reductase (QFR, FrdABCD) catalyzes the interconversion of fumarate and succinate at a covalently attached FAD within the FrdA subunit. The SdhE assembly factor enhances covalent flavinylation of Complex II homologs, but the mechanisms underlying the covalent attachment of FAD remain to be fully elucidated. Here, we explored the mechanisms of covalent flavinylation of the E. coli QFR FrdA subunit. Using a ΔsdhE E. coli strain, we show that the requirement for the assembly factor depends on the cellular redox environment. We next identified residues important for the covalent attachment and selected the FrdA E245 residue, which contributes to proton shuttling during fumarate reduction, for detailed biophysical and structural characterization. We found that QFR complexes containing FrdA E245Q have a structure similar to that of the WT flavoprotein, but lack detectable substrate binding and turnover. In the context of the isolated FrdA subunit, the anticipated assembly intermediate during covalent flavinylation, FrdA E245 variants had stability similar to that of WT FrdA, contained noncovalent FAD, and displayed a reduced capacity to interact with SdhE. However, small-angle X-ray scattering (SAXS) analysis of WT FrdA cross-linked to SdhE suggested that the FrdA E245 residue is unlikely to contribute directly to the FrdA-SdhE protein-protein interface. We also found that no auxiliary factor is absolutely required for flavinylation, indicating that the covalent flavinylation is autocatalytic. We propose that multiple factors, including the SdhE assembly factor and bound dicarboxylates, stimulate covalent flavinylation by preorganizing the active site to stabilize the quinone-methide intermediate.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2018

Crystal structure of the m4-1BB/4-1BBL complex reveals an unusual dimeric ligand that undergoes structural changes upon 4-1BB receptor binding

The interaction between the receptor 4-1BB and its ligand 4-1BBL provides co-stimulatory signals for T-cell activation and proliferation. However, differences in the mouse and human molecules might result in differential engagement of this pathway. Here, we report the crystal structure of mouse 4-1BBL and of the mouse 4-1BB/4-1BBL complex, which together provided insights into the molecular mechanism by which m4-1BBL and its cognate receptor recognize each other. Unlike all human or mouse tumor necrosis factor ligands that form noncovalent and mostly trimeric assemblies, the m4-1BBL structure formed a disulfide-linked dimeric assembly. The structure disclosed that certain differences in the amino acid composition along the intramolecular interface, together with two specific residues (Cys-246 and Ser-256) present exclusively in m4-1BBL, are responsible for this unique dimerization. Unexpectedly, upon m4-1BB binding, m4-1BBL undergoes structural changes within each protomer; moreover, the individual m4-1BBL protomers rotate relative to each other, yielding a dimerization interface with more inter-subunit interactions. We also observed that in the m4-1BB/4-1BBL complex, each receptor monomer binds exclusively to a single ligand subunit with contributions of cysteine-rich domain 1 (CRD1), CRD2, and CRD3. Furthermore, structure-guided mutagenesis of the binding interface revealed that novel binding interactions with the GH loop, rather than the DE loop, are energetically critical and define the m4-1BB receptor selectivity for m4-1BBL. As a result, a comparison with the human 4-1BB/4-1BBL complex highlighted several differences between the ligand- and receptor-binding interfaces, providing an explanation for the absence of inter-species cross-reactivity between human and mouse 4-1BB and 4-1BBL molecules.

4-1BB↗

DOE OSTI2019

Crystal structure of bacterial cytochrome bc 1 in complex with azoxystrobin reveals a conformational switch of the Rieske iron–sulfur protein subunit

Cytochrome bc 1 complexes (cyt bc 1 ), also known as complex III in mitochondria, are components of the cellular respiratory chain and of the photosynthetic apparatus of non-oxygenic photosynthetic bacteria. They catalyze electron transfer (ET) from ubiquinol to cytochrome c and concomitantly translocate protons across the membrane, contributing to the cross-membrane potential essential for a myriad of cellular activities. This ET-coupled proton translocation reaction requires a gating mechanism that ensures bifurcated electron flow. In this study, we report the observation of the Rieske iron–sulfur protein (ISP) in a mobile state, as revealed by the crystal structure of cyt bc 1 from the photosynthetic bacterium Rhodobacter sphaeroides in complex with the fungicide azoxystrobin. Unlike cyt bc 1 inhibitors stigmatellin and famoxadone that immobilize the ISP, azoxystrobin causes the ISP-ED to separate from the cyt b subunit and to remain in a mobile state. Analysis of anomalous scattering signals from the iron–sulfur cluster of the ISP suggests the existence of a trajectory for electron delivery. This work supports and solidifies the hypothesis that the bimodal conformation switch of the ISP provides a gating mechanism for bifurcated ET, which is essential to the Q-cycle mechanism of cyt bc 1 function.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Cryogenic and Temperature-Dependent Photoelectron Spectroscopy of Metal Complexes

Negative ion photoelectron spectroscopy (NIPES) coupled with electrospray ionization (ESI) has been proved to be a powerful gas-phase spectroscopic tool for characterizing electronic structures and chemical bonding of a variety of cluster anions and corresponding neutral radicals involved in the condensed phase reactions and transformations. Since the acquisition of cryogenic and temperature-controlling capabilities, broader range of research scope has been covered. This review summarizes our recent investigations on metal complexes employing cryogenic ESI-NIPES that provide us essential information towards understanding complicated condensed phase reactions including hydrocarbon activations and electron transfer reactions, and afford us spectroscopic probe of highly reactive transient species and intimate redox pairs. Special attention has been drawn to connect gas phase photodetachment processes with solution phase redox reactions. Photodetachment of transition metal-EDTA complexes has been systematically investigated to model the sequential oxidation reactions of these species in solutions. The obtained gas phase electron affinity (EA) is compared with the solution redox potential (E1/2) and the metal ionization potential (IP) for several series of homologous metal complexes to emphasize their intrinsic correlations with deviations being largely modulated by different degrees of ligand participations.

Yuan, Qinqin↗

DOE OSTI2019

SGEF forms a complex with Scribble and Dlg1 and regulates epithelial junctions and contractility

The canonical Scribble polarity complex is implicated in regulation of epithelial junctions and apical polarity. Here, we show that SGEF, a RhoG-specific GEF, forms a ternary complex with Scribble and Dlg1, two members of the Scribble complex. SGEF targets to apical junctions in a Scribble-dependent fashion and functions in the regulation of actomyosin-based contractility and barrier function at tight junctions as well as E-cadherin–mediated formation of adherens junctions. Surprisingly, SGEF does not control the establishment of polarity. However, in 3D cysts, SGEF regulates the formation of a single open lumen. Interestingly, SGEF’s nucleotide exchange activity regulates the formation and maintenance of adherens junctions, and in cysts the number of lumens formed, whereas SGEF’s scaffolding activity is critical for regulation of actomyosin contractility and lumen opening. We propose that SGEF plays a key role in coordinating junctional assembly and actomyosin contractility by bringing together Scribble and Dlg1 and targeting RhoG activation to cell–cell junctions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

The liquid state of FG-nucleoporins mimics permeability barrier properties of nuclear pore complexes

Nuclear pore complexes (NPCs) regulate all cargo traffic across the nuclear envelope. The transport conduit of NPCs is highly enriched in disordered phenylalanine/glycine-rich nucleoporins (FG-Nups), which form a permeability barrier of still elusive and highly debated molecular structure. Here we present a microfluidic device that triggered liquid-to-liquid phase separation of FG-Nups, which yielded droplets that showed typical properties of a liquid state. On the microfluidic chip, droplets were perfused with different transport-competent or -incompetent cargo complexes, and then the permeability barrier properties of the droplets were optically interrogated. We show that the liquid state mimics permeability barrier properties of the physiological nuclear transport pathway in intact NPCs in cells: that is, inert cargoes ranging from small proteins to large capsids were excluded from liquid FG-Nup droplets, but functional import complexes underwent facilitated import into droplets. Collectively, these data provide an experimental model of how NPCs can facilitate fast passage of cargoes across an order of magnitude in cargo size.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Microstate distinguishability, quantum complexity, and the eigenstate thermalization hypothesis

In this work, we use quantum complexity theory to quantify the difficulty of distinguishing eigenstates obeying the eigenstate thermalization hypothesis (ETH). After identifying simple operators with an algebra of low-energy observables and tracing out the complementary high-energy Hilbert space, the ETH leads to an exponential suppression of trace distance between the coarse grained eigenstates. Conversely, we show that an exponential hardness of distinguishing between states implies ETH-like matrix elements. Finally, the BBBV lower bound on the query complexity of Grover search then translates directly into a complexity-theoretic statement lower bounding the hardness of distinguishing these reduced states

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Understanding polaronic transport in complex oxides by combining precise synthesis and first-principles many-body theory

In complex oxides, charge carriers often couple strongly with lattice vibrations to form polarons–entangled electron–phonon quasiparticles whose transport properties remain difficult to characterize. Experimental access to intrinsic polaronic transport requires ultraclean samples, while theoretical description demands methods beyond low-order perturbation theory. Here, we show a predictive theory–experiment workflow to study polaron transport in complex oxides. Focusing on a prototypical polaronic oxide, anatase TiO 2 , we combine growth of high-quality oxygen-vacancy-doped films using hybrid molecular beam epitaxy with a first-principles electron–phonon diagrammatic Monte-Carlo (FEP-DMC) framework recently developed for accurate polaron predictions. Our films exhibit record-high electron mobility for anatase TiO 2 , in excellent agreement with FEP-DMC calculations conducted prior to experiment, which predict a room-temperature mobility of 45 ± 15 cm −2 V −1 s −1 and a mobility-temperature scaling of μ ∝ T −1.9 ± 0.077 . Microscopic analysis using scanning transmission electron microscopy and x-ray photoelectron spectroscopy reveals the role of oxygen vacancies in modulating transport at lower temperatures. FEP-DMC further provides quantitative insight into polaron formation energy, phonon cloud distribution, lattice distortion around the polaron, and the polaronic contribution to mobility. Together, these results provide a deeper microscopic understanding of large-polaron transport in a complex oxide and provide the blueprint to characterize other polaronic materials.

anatase TiO2↗

DOE OSTI2025

Many-body expansion based machine learning models for octahedral transition metal complexes

Abstract Graph-based machine learning (ML) models for material properties show great potential to accelerate virtual high-throughput screening of large chemical spaces. However, in their simplest forms, graph-based models do not include any 3D information and are unable to distinguish stereoisomers such as those arising from different orderings of ligands around a metal center in coordination complexes. In this work we present a modification to revised autocorrelation descriptors, a molecular graph featurization method, for predicting spin state dependent properties of octahedral transition metal complexes (TMCs). Inspired by analytical semi-empirical models for TMCs, the new modeling strategy is based on the many-body expansion (MBE) and allows one to tune the captured stereoisomer information by changing the truncation order of the MBE. We present the necessary modifications to include this approach in two commonly used ML methods, kernel ridge regression and feed-forward neural networks. On a test set composed of all possible isomers of binary TMCs, the best MBE models achieve mean absolute errors (MAEs) of 2.75 kcal mol −1 on spin-splitting energies and 0.26 eV on frontier orbital energy gaps, a 30%–40% reduction in error compared to models based on our previous approach. We also observe improved generalization to previously unseen ligands where the best-performing models exhibit MAEs of 4.00 kcal mol −1 (i.e. a 0.73 kcal mol −1 reduction) on the spin-splitting energies and 0.53 eV (i.e. a 0.10 eV reduction) on the frontier orbital energy gaps. Because the new approach incorporates insights from electronic structure theory, such as ligand additivity relationships, these models exhibit systematic generalization from homoleptic to heteroleptic complexes, allowing for efficient screening of TMC search spaces.

Meyer, Ralf (ORCID:0000000322360261)↗

DOE OSTI2025

Leveraging dendritic complexity for neuromorphic computing

Abstract Beyond-von Neumann computing approaches are necessary to sustain the growth of microelectronics and the increasing appetite for artificial intelligence/machine learning algorithms. Neuromorphic computing is an emerging paradigm that takes inspiration from the brain to provide a path forward to improve the computational efficiency and computational density of next-generation computing architectures. In nature, we observe brains performing complex computations with a much smaller energy footprint than conventional computing approaches. Current neuromorphic systems are focused primarily on scalability, namely, increasing the number of computational units (neurons) and connections between units (synapses). However, for brain-like cognition and efficiency in next-generation computing hardware, we need increased complexity in function, as well as improved connection density for scalability. Here, we present our work that aims to incorporate dendrites for ‘compute-on-wire’ in neuromorphic architectures to increase the computational complexity (e.g. number of programmable parameters, nonlinear dynamics) as well as computational efficiency (energy/compute) of artificial neural networks (ANNs). We do this by showcasing neuromorphic dendrite elements that can be leveraged for various applications. We will present examples of neuroscience-inspired direction-selective circuits and an ANN with active dendrites leveraging shunting inhibition. We also demonstrate the benefits of using dendrites in deep neural networks. To conclude, we discuss how we can utilize emerging hardware devices in these systems and design next-generation neuromorphic architectures with dendrites.

Cardwell, Suma G. (ORCID:0000000226575545)↗

DOE OSTI2019

Joint linkage and association mapping of complex traits in shrub willow (Salix purpurea L.)

Abstract Background and Aims Increasing energy demands and the necessity to reduce greenhouse gas emissions are key motivating factors driving the development of lignocellulosic crops as an alternative to non-renewable energy sources. The effects of global climate change will require a better understanding of the genetic basis of complex adaptive traits to breed more resilient bioenergy feedstocks, like willow (Salix spp.). Shrub willow is a sustainable and dedicated bioenergy crop, bred to be fast-growing and high-yielding on marginal land without competing with food crops. In a rapidly changing climate, genomic advances will be vital for the sustained improvement of willow and other non-model bioenergy crops. Here, joint genetic mapping was used to exploit genetic variation garnered from both recent and historical recombination events in S. purpurea. Methods A panel of North American naturalized S. purpurea accessions and full-sib F2S. purpurea population were genotyped and phenotyped for a suite of morphological, physiological, pest and disease resistance, and wood chemical composition traits, collected from multi-environment and multi-year replicated field trials. Controlling for population stratification and kinship in the association panel and spatial variation in the F2, a comprehensive mixed model analysis was used to dissect the complex genetic architecture and plasticity of these important traits. Key Results Individually, genome-wide association (GWAS) models differed in terms of power, but the combined approach, which corrects for yearly and environmental co-factors across datasets, improved the overall detection and resolution of associated loci. Although there were few significant GWAS hits located within support intervals of QTL for corresponding traits in the F2, many large-effect QTL were identified, as well as QTL hotspots. Conclusions This study provides the first comparison of linkage analysis and linkage disequilibrium mapping approaches in Salix, and highlights the complementarity and limits of these two methods for elucidating the genetic architecture of complex bioenergy-related traits of a woody perennial breeding programme.

Plant Sciences↗

DOE OSTI2022

Inexact Newton-CG algorithms with complexity guarantees

Abstract We consider variants of a recently developed Newton-CG algorithm for nonconvex problems (Royer, C. W. & Wright, S. J. (2018) Complexity analysis of second-order line-search algorithms for smooth nonconvex optimization. SIAM J. Optim., 28, 1448–1477) in which inexact estimates of the gradient and the Hessian information are used for various steps. Under certain conditions on the inexactness measures, we derive iteration complexity bounds for achieving $\epsilon $-approximate second-order optimality that match best-known lower bounds. Our inexactness condition on the gradient is adaptive, allowing for crude accuracy in regions with large gradients. We describe two variants of our approach, one in which the step size along the computed search direction is chosen adaptively, and another in which the step size is pre-defined. To obtain second-order optimality, our algorithms will make use of a negative curvature direction on some steps. These directions can be obtained, with high probability, using the randomized Lanczos algorithm. In this sense, all of our results hold with high probability over the run of the algorithm. We evaluate the performance of our proposed algorithms empirically on several machine learning models. Our approach is a first attempt to introduce inexact Hessian and/or gradient information into the Newton-CG algorithm of Royer & Wright (2018, Complexity analysis of second-order line-search algorithms for smooth nonconvex optimization. SIAM J. Optim., 28, 1448–1477).

Mathematics↗