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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Computational Complexity of Neuromorphic Algorithms

Neuromorphic computing has several characteristics that make it an extremely compelling computing paradigm for post Moore computation. Some of these characteristics include intrinsic parallelism, inherent scalability, collocated processing and memory, and event-driven computation. While these characteristics impart energy efficiency to neuromorphic systems, they do come with their own set of challenges. One of the biggest challenges in neuromorphic computing is to establish the theoretical underpinnings of the computational complexity of neuromorphic algorithms. In this paper, we take the first steps towards defining the space and time complexity of neuromorphic algorithms. Specifically, we describe a model of neuromorphic computation and state the assumptions that govern the computational complexity of neuromorphic algorithms. Next, we present a theoretical framework to define the computational complexity of a neuromorphic algorithm. We explicitly define what space and time complexities mean in the context of neuromorphic algorithms based on our model of neuromorphic computation. Finally, we leverage our approach and define the computational complexities of six neuromorphic algorithms: constant function, successor function, predecessor function, projection function, neuromorphic sorting algorithm and neighborhood subgraph extraction algorithm.

Date, Prasanna↗
DOE OSTI2021

Computational Spectroscopy of the Cr–Cr Bond in Coordination Complexes

In this work, we report the accurate computational vibrational analysis of the Cr–Cr bond in dichromium complexes using second-order multireference complete active space methods (CASPT2), allowing direct comparison with experimental spectroscopic data both to facilitate interpreting the low-energy region of the spectra and to provide insights into the nature of the bonds themselves. Recent technological development by the authors has realized such computation for the first time. Accurate simulation of the vibrational structure of these compounds has been hampered by their notorious multiconfigurational electronic structure that yields bond distances that do not correlate with bond order. Some measured Cr–Cr vibrational stretching modes, ν(Cr 2 ), have suggested weaker bonding, even for so-called ultrashort Cr–Cr bonds, while others are in line with the bond distance. Here, we optimize geometries and compute ν(Cr 2 ) with CASPT2 for three well-characterized complexes, Cr 2 (O 2 CCH 3 ) 4 (H 2 O) 2 , Cr 2 (mhp) 4 , and Cr 2 (dmp) 4 . We obtain CASPT2 harmonic ν(Cr 2 ) modes in good agreement with experiment at 282 cm –1 for Cr 2 (mhp) 4 and 353 cm –1 for Cr 2 (dmp) 4 , compute 50 Cr and 54 Cr isotope shifts, and demonstrate that the use of the so-called IPEA shift leads to improved Cr–Cr distances. Additionally, normal mode sampling was used to estimate anharmonicity along ν(Cr 2 ), leading to an anharmonic mode of 272 cm –1 for Cr 2 (mhp) 4 and 333 cm –1 for Cr 2 (dmp) 4 .

36 MATERIALS SCIENCE↗
DOE OSTI2022

Charge-Transfer Luminescence in a Molecular Donor–Acceptor Complex: Computational Insights

Donor–acceptor molecular complexes are a popular class of materials utilizing charge-transfer states for practical applications. A recent class of donor–acceptor dyads based on the fluorescent BODIPY functionalized with triphenylamine (TPA) shows the peculiar property of dual fluorescence. It is hypothesized that instead of the sensitized charge-transfer state being optically dark, it provides an additional bright radiative pathway. In this study, we use time-dependent density functional theory to characterize the energetic alignment of excitonic and charge-transfer states in a BODIPY-TPA molecular complex. We observe that using a long-range exchange corrected functional in combination with state-specific solvation scheme gives a qualitatively correct alignment of the exciton and charge-transfer states and an enhancement in oscillator strength for the equilibrium solvated charge-transfer state, in agreement with experiment. Furthermore, this work provides rationalization of charge-transfer state emission and provides a foundation to explore charge-transfer using ab initio excited-state nonadiabatic dynamics.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Quantum magic and computational complexity in the neutrino sector

We consider the quantum magic in systems of dense neutrinos undergoing coherent flavor transformations, relevant for supernova and neutron-star binary mergers. Mapping the three-flavor-neutrino system to qutrits, the evolution of quantum magic is explored in the single scattering angle limit for a selection of initial tensor-product pure states for 𝑁 𝜈 ≤ 8 neutrinos. For |𝜈𝑒⟩ ⊗𝑁𝜈 initial states, the magic, as measured by the 𝛼 = 2 stabilizer Renyi entropy ℳ 2 , is found to decrease with radial distance from the neutrino sphere, reaching a value that lies below the maximum for tensor-product qutrit states. Further, the asymptotic magic per neutrino, ℳ 2 /𝑁 𝜈 , decreases with increasing 𝑁 𝜈 . In contrast, the magic evolving from states containing all three flavors reaches values only possible with entanglement, with the asymptotic ℳ 2 /𝑁 𝜈 increasing with 𝑁 𝜈 . These results highlight the connection between the complexity in simulating quantum physical systems and the parameters of the Standard Model.

computational complexity↗
DOE OSTI2024

Glassy Word Problems: Ultraslow Relaxation, Hilbert Space Jamming, and Computational Complexity

We introduce a family of local models of dynamics based on “word problems” from computer science and group theory, for which we can place rigorous lower bounds on relaxation timescales. These models can be regarded either as random circuit or local Hamiltonian dynamics and include many familiar examples of constrained dynamics as special cases. The configuration space of these models splits into dynamically disconnected sectors, and for initial states to relax, they must “work out” the other states in the sector to which they belong. When this problem has a high time complexity, relaxation is slow. In some of the cases we study, this problem also has high space complexity. When the space complexity is larger than the system size, an unconventional type of jamming transition can occur, whereby a system of a fixed size is not ergodic but can be made ergodic by appending a large reservoir of sites in a trivial product state. This finding manifests itself in a new type of Hilbert space fragmentation that we call fragile fragmentation. We present explicit examples where slow relaxation and jamming strongly modify the hydrodynamics of conserved densities. In one example, density modulations of wave vector q exhibit almost no relaxation until times O ( exp ( 1 / q ) ) , at which point they abruptly collapse. We also comment on extensions of our results to higher dimensions. Published by the American Physical Society 2024

Physics↗
DOE OSTI2021

Scalable Approaches to Selecting Key Entities in Large Networked Infrastructure Systems

This work aims at bringing advances in discrete optimization algorithms to solving practical engineering problems at scale. Often times, in many engineering design problems, there is a need to select a small set of influential or representative elements from a large ground set of entities in an optimal fashion. Submodular optimization provides for a formal way to solve such problems. Common examples with infrastructure systems involve sensor placement and identification of key entities with certain objectives. However, scaling these approaches to large infrastructure systems can be challenging because of the high computational complexity of the overall framework that include the optimization algorithms as well as high-complexity compute-oracles that provide the necessary objective function values. In this work, we explore a well-studied and widely-applicable paradigm, namely leader-selection in a multi-agent networked setting in the context of scalable methodologies. We demonstrate novel frameworks that utilize variations of accelerated submodular optimization algorithms along with linear-algebraic methods that can help accelerate the oracle computations. We further explore this combination in conjunction with graph partitioning paradigms to take advantage of the accelerated algorithms in a distributed setting. Finally we demonstrate the key findings on a practical problem in an operational setting. For this, we leverage an example road network with approximately 18k nodes and 27k edges in a traffic control application, where we seek a limited number of k=200 key intersections. This problem can be solved in a serial setting in just under 5 hours providing more than 2 orders of magnitude speed-up over methods that do not consider acceleration techniques.

Visweswara Sathanur, Arun↗
DOE OSTI2023

Computing the Relative Affinity of Chlorophylls a and b to Light-Harvesting Complex II

In plants and algae, the primary antenna protein bound to photosystem II is light-harvesting complex II (LHCII), a pigment–protein complex that binds eight chlorophyll (Chl) a molecules and six Chl b molecules. Chl a and Chl b differ only in that Chl a has a methyl group (–CH 3 ) on one of its pyrrole rings, while Chl b has a formyl group (–CHO) at that position. This blue-shifts the Chl b absorbance relative to Chl a . It is not known how the protein selectively binds the right Chl type at each site. Knowing the selection criteria would allow the design of light-harvesting complexes that bind different Chl types, modifying an organism to utilize the light of different wavelengths. The difference in the binding affinity of Chl a and Chl b in pea and spinach LHCII was calculated using multiconformation continuum electrostatics and free energy perturbation. Both methods have identified some Chl sites where the bound Chl type ( a or b ) has a significantly higher affinity, especially when the protein provides a hydrogen bond for the Chl b formyl group. However, the Chl a sites often have little calculated preference for one Chl type, so they are predicted to bind a mixture of Chl a and b . The electron density of the spinach LHCII was reanalyzed, which, however, confirmed that there is negligible Chl b in the Chl a -binding sites. Finally, it is suggested that the protein chooses the correct Chl type during folding, segregating the preferred Chl to the correct binding site.

chemical calculations↗
DOE OSTI2021

Systems and methods for rapid processing and storage of data

Systems and methods of building massively parallel computing systems using low power computing complexes in accordance with embodiments of the invention are disclosed. A massively parallel computing system in accordance with one embodiment of the invention includes at least one Solid State Blade configured to communicate via a high performance network fabric. In addition, each Solid State Blade includes a processor configured to communicate with a plurality of low power computing complexes interconnected by a router, and each low power computing complex includes at least one general processing core, an accelerator, an I/O interface, and cache memory and is configured to communicate with non-volatile solid state memory.

Stalzer, Mark A.↗
DOE OSTI2025

Sign Problem in Tensor-Network Contraction

We investigate how the computational difficulty of contracting tensor networks depends on the sign structure of the tensor entries. Using results from computational complexity, we observe that the approximate contraction of tensor networks with only positive entries has lower computational complexity as compared to tensor networks with general real or complex entries. This raises the question of how this transition in computational complexity manifests itself in the hardness of different tensor-network-contraction schemes. We pursue this question by studying random tensor networks with varying bias toward positive entries. First, we consider contraction via Monte Carlo sampling and find that the transition from hard to easy occurs when the tensor entries become predominantly positive; this can be understood as a tensor-network manifestation of the well-known negative-sign problem in quantum Monte Carlo. Second, we analyze the commonly used contraction based on boundary tensor networks. The performance of this scheme is governed by the number of correlations in contiguous parts of the tensor network (which by analogy can be thought of as entanglement). Remarkably, we find that the transition from hard to easy—i.e., from a volume-law to a boundary-law scaling of entanglement—already occurs for a slight bias of the tensor entries toward a positive mean, scaling inversely with the bond dimension D , and thus the problem becomes easy the earlier the larger D occurs. This is in contrast both to expectations and to the behavior found in Monte Carlo contraction, where the hardness at fixed bias increases with the bond dimension. To provide insight into this early breakdown of computational hardness and the accompanying entanglement transition, we construct an effective classical statistical-mechanical model that predicts a transition at a bias of the tensor entries of 1 / D , confirming our observations. We conclude by investigating the computational difficulty of computing expectation values of tensor-network wave functions (projected entangled-pair states, PEPSs) and find that in this setting, the complexity of entanglement-based contraction always remains low. We explain this by providing a local transformation that maps PEPS expectation values to a positive-valued tensor network. This not only provides insight into the origin of the observed boundary-law entanglement scaling but also suggests new approaches toward PEPS contraction based on positive decompositions. Published by the American Physical Society 2025

Chen, Jielun (ORCID:0000000178411545)↗
DOE OSTI2023

The Tiny Triplet Finder as a Versatile Track Segment Seeding Engine for Trigger Systems

In high energy physics experiment trigger systems, track segment seeding is a resource consuming function and the primary reason is the computing complexity of the segment finding process. As the Moore's Law is reaching its physical limit, reducing computing complexity should be carefully considered, rather than keep piling up silicon resources. The Tiny Triplet Finder is a scheme that reduces the computing complexity of the segment seeding. As a proof of concept, a 3D track segment seeding engine core based on the Tiny Triplet Finder has been implemented and tested in a low-cost FPGA device. The seeding engine is designed to preselect and group hits (stubs) from detector layers to feed subsequent track fitting stage. The seeding engine consists of a Hough transform space for r-z view and a Tiny Triplet Finder for r-phi view to implement 3D constraints. The seeding engine is organized as a pipeline so that each hit is processed in a single clock cycle. Taking advantage of the register-like storage block scheme which enables effectively resetting of a block RAM within a single clock cycle, clearing or refreshing the seeding engine takes only one clock cycles between two events. The Tiny Triplet Finder is also a generic coincidence finding scheme that can be used for many tasks. As a versatility demonstration, track segment finding performances for two distinctive detector geometries are tested in our seeding engine. In a collider barrel-layer geometry, the fake segment rates are studied for 3D (i.e., both r-phi and r-z views) and 2D (i.e., r-phi or r-z view only) configurations for high hit multiplicity events (>4000 hits/layer in the barrel region). Another detector geometry contains strip plane layers with timing information. The numbers of coincidences, both real or fake, with or without timing ("3D" or "2D") information at various hit multiplicities are studied.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

Efficient and Robust Jet Tagging at the LHC with Knowledge Distillation

The challenging environment of real-time data processing systems at the Large Hadron Collider (LHC) strictly limits the computational complexity of algorithms that can be deployed. For deep learning models, this implies that only models with low computational complexity that have weak inductive bias are feasible. To address this issue, we utilize knowledge distillation to leverage both the performance of large models and the reduced computational complexity of small ones. In this paper, we present an implementation of knowledge distillation, demonstrating an overall boost in the student models' performance for the task of classifying jets at the LHC. Furthermore, by using a teacher model with a strong inductive bias of Lorentz symmetry, we show that we can induce the same inductive bias in the student model which leads to better robustness against arbitrary Lorentz boost.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Trajectory prediction dimensionality reduction for low-cost connected automated vehicle systems

Here, to facilitate low-cost connected automated vehicle (CAV) system development, this study proposes two interpretable dimensionality reduction techniques in vehicle trajectory prediction, i.e., the piecewise Taylor series approximation (PTA) and the piecewise Fourier series approximation (PFA), to lower computation complexity, reduce device investment, and decrease computation energy consumption. Two benchmarks are developed, the long short-term memory (LSTM)-based model without dimensionality reduction and the LSTM-based model with encoder-decoder (a widely used dimensionality reduction technique). Results show that the four predictions have similar accuracy, and the training time (proportional to computation energy consumption) of models with dimensionality reduction techniques is greatly reduced. The reduction is even more significant when PTA/PFA is used. Sensitivity analysis advises PFA/PTA parameter selections to reduce computation complexity without significant loss of prediction accuracy. Further, the robustness of the LSTM PTA/PFA is proven by the investigation of data noises.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
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 OSTI2023

Bridge-Mediated Metal-to-Metal Electron and Hole Transfer in a Supermolecular Dinuclear Complex: A Computational Study Using Quantum Electron–Nuclear Dynamics

Bimetallic electron donor–acceptor complexes can facilitate electron and energy transfer with excellent structural control through synthetic design. In this work, we investigate the photochemical dynamics in a Ru–Cu bimetallic complex after photoexcitation of the Ru-centered charge transfer state. The physical underpinnings of the metal-to-metal directional charge transfer process are unraveled via analyses of the quantum electronic dynamics and electron–nuclear trajectories. Here, the effects of molecular vibrations in the photoexcited state on the charge transfer processes are also analyzed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

A time-parallel multiple-shooting method for large-scale quantum optimal control

Quantum optimal control plays a crucial role in quantum computing by providing the interface between compiler and hardware. Solving the optimal control problem is particularly challenging for multi-qubit gates, due to the exponential growth in computational complexity with the system's dimensionality and the deterioration of optimization convergence. To ameliorate the computational complexity of time-integration, this paper introduces a multiple-shooting approach in which the time domain is divided into multiple windows and the intermediate states at window boundaries are treated as additional optimization variables. Further, this enables parallel computation of state evolution across time-windows, significantly accelerating objective function and gradient evaluations. Since the initial state matrix in each window is only guaranteed to be unitary upon convergence of the optimization algorithm, the conventional gate trace infidelity is replaced by a generalized infidelity that is convex for non-unitary state matrices. Continuity of the state across window boundaries is enforced by equality constraints. A quadratic penalty optimization method is used to solve the constrained optimal control problem, and an efficient adjoint technique is employed to calculate the gradients in each iteration. We demonstrate the effectiveness of the proposed method through numerical experiments on quantum Fourier transform gates in systems with 2, 3, and 4 qubits, noting a speedup of 80x for evaluating the gradient in the 4-qubit case, highlighting the method's potential for optimizing control pulses in multi-qubit quantum systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Multisource Data Fusion Outage Location in Distribution Systems via Probabilistic Graphical Models

Efficient outage location is critical to enhancing the resilience of power distribution systems. However, accurate outage location requires combining massive evidence received from diverse data sources, including smart meter (SM) last gasp signals, customer trouble calls, social media messages, weather data, vegetation information, and physical parameters of the network. This is a computationally complex task due to the high dimensionality of data in distribution grids. In this paper, we propose a multi-source data fusion approach to locate outage events in partially observable distribution systems using Bayesian networks (BNs). A novel aspect of the proposed approach is that it takes multi-source evidence and the complex structure of distribution systems into account using a probabilistic graphical method. Our method can radically reduce the computational complexity of outage location inference in high-dimensional spaces. The graphical structure of the proposed BN is established based on the network’s topology and the causal relationship between random variables, such as the states of branches/customers and evidence. Utilizing this graphical model, accurate outage locations are obtained by leveraging a Gibbs sampling (GS) method, to infer the probabilities of de-energization for all branches. Compared with commonly-used exact inference methods that have exponential complexity in the size of the BN, GS quantifies the target conditional probability distributions in a timely manner. As a result, a case study of several real-world distribution systems is presented to validate the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗