Single Time Step Research Articles

Real-Time Dyson-Expansion Scheme: Efficient Inclusion of Dynamical Correlations in Nonequilibrium Spectral Properties.

Time-resolved photoemission spectroscopy is the key technique to probe the real-time nonequilibrium dynamics of electronic states. Theoretical predictions of the time dependent spectral function for realistic systems is however, a challenge. Employing the Kadanoff-Baym equations to find this quantity results in a cubic scaling in the total number of time steps, quickly becoming prohibitive and often fail quantitatively and even qualitatively. In comparison, mean-field methods have more favorable numerical scaling both in the number of time steps and in the complexity associated with the cost of evolving for a single time step, however they miss key spectral properties such as emergent spectral features. Here we present a scheme that allows for the inclusion of dynamical correlations to the spectral function while maintaining the same scaling in the number of time steps as for mean-field approaches, while capturing the emergent physics. Further, the scheme can be efficiently implemented on top of equilibrium real-time many-body perturbation theory schemes and codes. We see excellent agreement with exact results for test systems. Furthermore, we exemplify the method on a periodic system and demonstrate clear evidence that our proposed scheme produces complex spectral features including excitonic band replicas, features that are not observed using static mean-field approaches.

Efficient quantum lattice gas automata

This study presents a novel quantum algorithm for lattice gas automata simulation with a single time step, demonstrating logarithmic complexity in terms of CX gates. The algorithm is composed of three main steps: collision, mapping, and propagation. A computational complexity analysis and a comparison using different error rates and number of shots are provided. Despite the impact of noise, our findings indicate that accurate simulations could be achieved already on current noisy devices. This suggests potential for efficient simulation of classical fluid dynamics using quantum lattice gas automata, conditional on advancements to expand the current method to multiple time steps and state preparation.

Heat pump digital twin: An accurate neural network model for heat pump behaviour prediction

Heat pumps are key in reaching the carbon emission reduction goals and can also be used to provide energy flexibility services. In this context, accurate heat pump control is crucial and requires a detailed heat pump model. Such a model should enable to take into account the latest information of the system in order to determine the expected heat pump behaviour. Several works already proposed a variety of heat pump models, but mainly adopt time steps above fifteen minutes. Given these larger time steps, the effects of the internal heat pump control strategies such as the compressor ramping rate or variable speed pump control logics are neglected. Hence, energy management systems are not able to obtain accurate information on the expected heat pump response when applying a certain control signal. Therefore, this work investigates the role of neural networks in developing a digital twin of a water/water heat pump, which adopts a time step of one minute and uses experimental data from a hardware-in-the-loop set-up. An architecture with six inputs and six outputs is proposed. The inputs contain the measured flow rates and inlet temperatures at both the evaporator and condenser, but also the measured and requested condenser outlet temperatures. The outputs of the model are the thermal capacity and electricity consumption, accompanied by the flow rates and outlet temperatures at both the evaporator and condenser. Two different types of neural networks are investigated, i.e. (1) feedforward neural networks and (2) long short-term memory neural networks using several time horizons regarding the previous heat pump operation. The models are evaluated for both a single time step ahead (monitoring) and multiple time steps ahead (behaviour prediction). Regarding the latter aspect, a long short-term memory neural network using the latest 60 min of operational data achieved the following prediction errors: electrical power consumption within ±10 % for 79.70 % of the time, condenser flow rate within ±10 % for 89.81 % of the time and condenser outlet temperature within ±1 % for 83.89 % of the time. The ability of long short-term memory neural networks to take into account previous control decisions is seen key in achieving reliable multiple time step ahead predictions. Finally, the replicability of the model to be used for a different heat emission system is also evaluated. Results show a poorer performance as the model is trained and tested on a different heat emission system, but indicate the potential for replicability when enriching the training dataset.

A Solution to Dynamic Weapon Assignment Problem Based on Game Theory for Naval Platforms

Weapon target assignment is a critical challenge in military contexts. Traditionally, commanding officers manually decide weapon assignments, but the problem’s complexity has grown over time. To address this, automated systems have been introduced. These systems fall into two categories, which are static (time-independent) and dynamic (considering changes over time). Static systems solve the problem for a single time step without considering temporal changes. Dynamic systems incorporate time as a variable, adapting to evolving scenarios. Two main approaches exist, which are asset-based and target-based. Asset-based approach maximizes the survival probability of assets, which is our focus in this study. We propose a solution using game theory that spans the entire area and all time frames. We employ game theory, treating continuous functions of time as utility functions for vessels. Continuous probability-to-kill values for weapons are defined across the area. Threat trajectories yield continuous kill probabilities for the weapons, translating to vessel utility. To avoid inefficiencies, we align individual vessel utility with global utility. The Nash Equilibrium provides the optimal weapon assignment strategy. Our study uses a naval environment for analysis. In summary, our research leverages game theory to dynamically assign weapons to naval vessels, aiming to maximize asset survival.

Linear symmetric self-selecting 14-bit kinetic molecular memristors.

Artificial Intelligence (AI) is the domain of large resource-intensive data centres that limit access to a small community of developers1,2. Neuromorphic hardware promises greatly improved space and energy efficiency for AI but is presently only capable of low-accuracy operations, such as inferencing in neural networks3-5. Core computing tasks of signal processing, neural network training and natural language processing demand far higher computing resolution, beyond that of individual neuromorphic circuit elements6-8. Here we introduce an analog molecular memristor based on a Ru-complex of an azo-aromatic ligand with 14-bit resolution. Precise kinetic control over a transition between two thermodynamically stable molecular electronic states facilitates 16,520 distinct analog conductance levels, which can be linearly and symmetrically updated or written individually in one time step, substantially simplifying the weight update procedure over existing neuromorphic platforms3. The circuit elements are unidirectional, facilitating a selector-less 64 × 64 crossbar-based dot-product engine that enables vector-matrix multiplication, including Fourier transform, in a single time step. We achieved more than 73 dB signal-to-noise-ratio, four orders of magnitude improvement over the state-of-the-art methods9-11, while consuming 460× less energy than digital computers12,13. Accelerators leveraging these molecular crossbars could transform neuromorphic computing, extending it beyond niche applications and augmenting the core of digital electronics from the cloud to the edge12,13.

Numerical integration of mechanical forces in center-based models for biological cell populations

Center-based models are used to simulate the mechanical behavior of biological cells during embryonic development or cancer growth. To allow for the simulation of biological populations potentially growing from a few individual cells to many thousands or more, these models have to be numerically efficient, while being reasonably accurate on the level of individual cell trajectories. In this work, we increase the robustness, accuracy, and efficiency of the simulation of center-based models by choosing the time steps adaptively in the numerical method and comparing five different integration methods. We investigate the gain in using single rate time stepping based on local estimates of the numerical errors for the forward and backward Euler methods of first order accuracy and a Runge-Kutta method and the trapezoidal method of second order accuracy. Properties of the analytical solution such as convergence to steady state and conservation of the center of gravity are inherited by the numerical solutions. Furthermore, we propose a multirate time stepping scheme that simulates regions with high local force gradients (e.g. as they happen after cell division) with multiple smaller time steps within a larger single time step for regions with smoother forces. These methods are compared for a model system in numerical experiments. We conclude, for example, that the multirate forward Euler method performs better than the Runge-Kutta method for low accuracy requirements but for higher accuracy the latter method is preferred. Only with frequent cell divisions the method with a fixed time step is the best choice.

An ultraweak-local discontinuous Galerkin method for nonlinear biharmonic Schrödinger equations

This paper proposes and analyzes a fully discrete scheme for nonlinear biharmonic Schrödinger equations. We first write the single equation into a system of problems with second-order spatial derivatives and then discretize the space variable with an ultraweak discontinuous Galerkin scheme and the time variable with the Crank–Nicolson method. The proposed scheme proves to be computationally more efficient compared to the local discontinuous Galerkin method in terms of the number of equations needed to be solved at each single time step, and it is unconditionally stable without imposing any penalty terms. It also achieves optimal error convergence in L2 norm both in the solution and in the auxiliary variable with general nonlinear terms. We also prove several physically relevant properties of the discrete schemes, such as the conservation of mass and the Hamiltonian for the nonlinear biharmonic Schrödinger equations. Several numerical studies demonstrate and support our theoretical results.

Spatio-Temporal Pruning for Training Ultra-Low-Latency Spiking Neural Networks in Remote Sensing Scene Classification

In remote sensing scene classification (RSSC), restrictions on real-time processing on power consumption, performance, and resources necessitate the compression of neural networks. Unlike artificial neural networks (ANNs), spiking neural networks (SNNs) convey information through spikes, offering superior energy efficiency and biological plausibility. However, the high latency of SNNs restricts their practical application in RSSC. Therefore, there is an urgent need to research ultra-low-latency SNNs. As latency decreases, the performance of the SNN significantly deteriorates. To address this challenge, we propose a novel spatio-temporal pruning method that enhances the feature capture capability of ultra-low-latency SNNs. Our approach integrates spatial fundamental structures during the training process, which are subsequently pruned. We conduct a comprehensive evaluation of the impacts of these structures across classic network architectures, such as VGG and ResNet, demonstrating the generalizability of our method. Furthermore, we develop an ultra-low-latency training framework for SNNs to validate the effectiveness of our approach. In this paper, we successfully achieve high-performance ultra-low-latency SNNs with a single time step for the first time in RSSC. Remarkably, our SNN with one time step achieves at least 200 times faster inference time while maintaining a performance comparable to those of other state-of-the-art methods.

Treatment for the Singularity Problem in the Phase Segregation

In the Eulerian–Eulerian two-fluid model, comprising air and droplets, singularities often arise as the phase fraction of dispersed droplets approaches zero. The nonconservative momentum equations can address this issue, but it will lead to inaccurate solutions when encountering discontinuities. To tackle the singularity problem and ensure accurate solutions for the droplet field, a novel adaptive form of momentum equations is proposed. The adaptive form defaults to the conservative form and smoothly transitions to the phase-intensive form when the phase fraction falls below a critical value, specifically 1/1000 of the inlet. The LU-SGS algorithm, enhanced with the inner iteration step method, is employed for numerical solutions of the droplet field. Comparative analysis reveals that the discrepancy between the results obtained from the adaptive form and the conservative form is negligible, under 0.5‰. Notably, with larger Courant numbers, the conservative form diverges from waterless regions despite imposing the minimum phase fraction constraint. Conversely, the adaptive form consistently maintains a Courant number of five times or more, potentially exceeding a hundredfold in complex flows. Although the adaptive form moderately increases complexity and computational time for a single time step, the improvement of the maximum Courant number will bring significant computational efficiency advantages. Moreover, the adaptive form holds promise for application in various other multiphase flow scenarios.

Attention-Based Deep Spiking Neural Networks for Temporal Credit Assignment Problems.

The temporal credit assignment (TCA) problem, which aims to detect predictive features hidden in distracting background streams, remains a core challenge in biological and machine learning. Aggregate-label (AL) learning is proposed by researchers to resolve this problem by matching spikes with delayed feedback. However, the existing AL learning algorithms only consider the information of a single timestep, which is inconsistent with the real situation. Meanwhile, there is no quantitative evaluation method for TCA problems. To address these limitations, we propose a novel attention-based TCA (ATCA) algorithm and a minimum editing distance (MED)-based quantitative evaluation method. Specifically, we define a loss function based on the attention mechanism to deal with the information contained within the spike clusters and use MED to evaluate the similarity between the spike train and the target clue flow. Experimental results on musical instrument recognition (MedleyDB), speech recognition (TIDIGITS), and gesture recognition (DVS128-Gesture) show that the ATCA algorithm can reach the state-of-the-art (SOTA) level compared with other AL learning algorithms.

Variational quantum recurrent neural networks for multi-feature forecasting

Recurrent neural networks are a kind of recursion which takes sequence data as input and carries on the evolution of temporal dependency data. Variational quantum algorithms use classical computers as the quantum optimizer to update the circuit parameters. In this work, we propose a variational quantum algorithm of the recurrent neural network, which we dub VQRNN, to find approximate optima in the time series forecasting. Motivated by the variational quantum algorithms, we train classical activation functions to assist quantum computing. Here, unlike the quantum tensor networks (QTN) algorithm that predicts a single output feature with a single time step, our algorithm can forecast multi-output features by adjusting the recurrent hidden state. Finally, we deploy the QTN and VQRNN algorithms on the Origin Quantum platform with the numerical simulator backends using the Meteorological data set. Experimental results show that the atmospheric pressure prediction accuracy of VQRNN is 99.8864% in multi-feature forecasting tasks. In addition, we conclude that the variation-based model has an excellent performance in multi-feature output forecasting.

Discrete unified gas kinetic scheme for the solution of electron Boltzmann transport equationwith Callaway approximation.

Electrons are the carriers of heat and electricity in materials and exhibit abundant transport phenomena such as ballistic, diffusive, and hydrodynamic behaviors in systems with different sizes. The electron Boltzmann transport equation(eBTE) is a reliable model for describing electron transport, but it is a challenging problem to efficiently obtain the numerical solutions of the eBTE within one unified scheme involving ballistic, hydrodynamics, and/or diffusive regimes. In this work, a discrete unified gas kinetic scheme (DUGKS) in the finite-volume framework is developed based on the eBTE with the Callaway relaxation model for electron transport. By reconstructing the distribution function at the cell interface, the processes of electron drift and scattering are coupled together within a single time step. Numerical tests demonstrate that the DUGKS can be adaptively applied to multiscale electron transport, across different regimes.

Cournot Policy Model: Rethinking centralized training in multi-agent reinforcement learning

This work studies Centralized Training and Decentralized Execution (CTDE), which is a powerful mechanism to ease multi-agent reinforcement learning. Although the centralized evaluation ensures unbiased estimates of Q-value, peers with unknown policies make the decentralized policy far from the expectation. To make progress in more stabilized and effective joint policy, we develop a novel game framework, termed Cournot Policy Model, to enhance the CTDE-based multi-agent learning. Combining the game theory and reinforcement learning, we regard the joint decision-making in a single time step as a Cournot duopoly model, and then design a Hetero Variational Auto-Encoder to model the policies of peers in the decentralized execution. With a conditional policy, each agent is guided to a stable mixed-strategy equilibrium even though the joint policy evolves over time. We further demonstrate that such an equilibrium must exist in the case of centralized evaluation. We investigate the improvement of our method on existing centralized learning methods. The experimental results on a comprehensive collection of benchmarks indicate our approach consistently outperforms baseline methods.

An optimized time-adaptive aerothermal coupling calculation method for aerothermal analysis of disc cavity system

In order to further achieve the balance between the calculation accuracy and efficiency of the transient analysis of the aero-engine disc cavity system, an Optimized Time-adaptive Aerothermal Coupling calculation (OTAC) method has been proposed. It combines one-dimensional transient calculation of air system, Conventional Sequence Staggered (CSS) method, Time-adaptive Aerothermal Coupling calculation (TAC) method and differential evolution optimization algorithm to obtain an efficient and high-precision aerothermal coupling calculation method of air system. Considering both the heat conduction in the solid domain and the flow in the fluid domain as unsteady states in the OTAC, the interaction of fluid–solid information within a single coupling time step size was implemented based on the CSS method. Furthermore, the coupling time step size was automatically adjusted with the number of iterations by using the Proportional-Integral-Derivative (PID) controller. Results show that when compared with the traditional loosely coupling method with a fixed time step size, the computational accuracy and efficiency of the OTAC method are improved by 8.9% and 30%, respectively. Compared with the tight coupling calculation, the OTAC method can achieve a speedup of 1 to 2 orders of magnitude, while the calculation error is maintained within 6.1%.

Partitioned time couplings of an aero-mechanical wind turbine problem.

Wind turbine developments have led to more powerful offshore rotor systems, creating complex aero-hydro-servo-elastic behaviors that require numerical analysis. A mutliphysics problem can be modelled using several approaches: a “monolithic” method where the systems are considered as a unique block or a “partitioned coupling” where the different domains are solved sequentially. The latter is the retained technique for this work in which different solvers are related to distinct equations that require independent time discretisations. The focus is set on coupling a wind turbine’s mechanical solver with an aerodynamic code, the latter being modelled through an inviscid vortex method and the structural aspect using a finite element method. The study aims to present the implementation process and comparison of different time integration coupling schemes within a large wind turbine simulation framework where aeroelastic effects are studied on the IEA 15MW wind turbine. A ”Conventional Serial Staggered” (CSS) scheme is used as a reference coupling technique, allowing independent time integration while limiting coupling to a single time step. Alternatively, a resembling “subcycling” architecture is proposed and implemented to remedy cases with different temporal discretisations and reduce computational costs of CSS when using the inviscid vortex method.

A Multi-Time-Step Parallel Computing Method based on Overlapping Particles for DEM

The application of the discrete element method (DEM) to continuous medium problems is becoming increasingly widespread. In this work, a parallel computing method with multiple time steps based on overlapping particles is proposed. The domain decomposition method (DDM) with overlapping particles method is used to increase the speed up and shorten the computation time and meet the consistency requirements during data transmission. The multi-time-step method (MTSM) is adopted to tackle the matching of asynchronous step boundary. Data are exchanged at the boundaries in each subdomain with a message passing interface (MPI). The computational efficiency of different step ratios in both serial and parallel computing is studied respectively. Numerical examples show that the DEM can effectively handle large structure deformation problems, and provides a shorter calculation time than that of the finite element method (FEM). The DEM with multiple time steps in different subdomains effectively reduces the computation time than that with a single time step in the entire domain. Under fixed step ratio conditions, using parallel computing can save more time than serial computing. This work develops ideas for expanding the application of DEM for large engineering problems.

Quantum Control of Radical-Pair Dynamics beyond Time-Local Optimization

We realize arbitrary-wave-form-based control of spin-selective recombination reactions of radical pairs in the low-magnetic-field regime. To this end, we extend the gradient-ascent pulse engineering (GRAPE) paradigm to allow for optimizing reaction yields. This overcomes drawbacks of previously suggested time-local optimization approaches for the reaction control of radical pairs, which were limited to high biasing fields. We demonstrate how efficient time-global optimization of the recombination yields can be realized by gradient-based methods augmented by time blocking, sparse sampling of the yield, and evaluation of the central single time-step propagators and their Fréchet derivatives using iterated Trotter-Suzuki splittings. Results are shown for both a toy model, previously used to demonstrate coherent control of radical-pair reactions in the simpler high-field scenario and, furthermore, for a realistic exciplex-forming donor-acceptor system comprising 16 nuclear spins. This raises prospects for the spin control of actual radical-pair systems in ambient magnetic fields, by suppressing or boosting radical reaction yields using purpose-specific radio-frequency wave forms, paving the way for reaction-yield-dependent quantum magnetometry and potentially applications of quantum control to biochemical radical-pair reactions. We demonstrate the latter aspect for two radical pairs implicated in quantum biology. Published by the American Physical Society 2024

On Computing Makespan-Optimal Solutions for Generalized Sliding-Tile Puzzles

In the 15-puzzle game, 15 labeled square tiles are reconfigured on a 4 × 4 board through an escort, wherein each (time) step, a single tile neighboring it may slide into it, leaving the space previously occupied by the tile as the new escort. We study a generalized sliding-tile puzzle (GSTP) in which (1) there are 1+ escorts and (2) multiple tiles can move synchronously in a single time step. Compared with popular discrete multi-agent/robot motion models, GSTP provides a more accurate model for a broad array of high-utility applications, including warehouse automation and autonomous garage parking, but is less studied due to the more involved tile interactions. In this work, we analyze optimal GSTP solution structures, establishing that computing makespan optimal solutions for GSTP is NP-complete and developing polynomial time algorithms yielding makespans approximating the minimum with expected/high probability constant factors, assuming randomized start and goal configurations.

Topological defects in Floquet circuits

We introduce a Floquet circuit describing the driven Ising chain with topological defects. The corresponding gates include a defect that flips spins as well as the duality defect that explicitly implements the Kramers-Wannier duality transformation. The Floquet unitary evolution operator commutes with such defects, but the duality defect is not unitary, as it projects out half the states. We give two applications of these defects. One is to analyze the return amplitudes in the presence of “space-like” defects stretching around the system. We verify explicitly that the return amplitudes are in agreement with the fusion rules of the defects. The second application is to study unitary evolution in the presence of “time-like” defects that implement anti-periodic and duality-twisted boundary conditions. We show that a single unpaired localized Majorana zero mode appears in the latter case. We explicitly construct this operator, which acts as a symmetry of this Floquet circuit. We also present analytic expressions for the entanglement entropy after a single time step for a system of a few sites, for all of the above defect configurations.

Balancing: A solution to our distorted indices of transient dynamics

AbstractBecause populations are at the mercy of random disturbances large and small, they rarely, if ever, converge on predicted long‐term behaviors. Therefore, when employing matrix population models, ecologists study the dynamics of populations that depart from stable distributions. Necessary for such studies are indices of transient dynamics that measure the size of short‐term population fluctuations. These indices advance our understanding of population dynamics by revealing that population growth rate in a single timestep can far exceed the stable population growth rate. Despite their value, indices of transient behavior possess two major shortcomings: they are scale dependent and easily distorted by outsized population classes. Distortion occurs whenever immature classes, due to their sheer size, carry greater weight in the calculation of population size than mature classes. Beluga sturgeon (Huso huso), for example, have an immature age class (eggs) that is several orders of magnitude larger than its mature age classes. To remove the undue influence of outsized classes, I use balancing, which rescales classes by the stable population distribution and makes the indices of transient dynamics scale invariant. I apply balancing to 1800 population projection matrices for various species across the Animal Kingdom, using reactivity and the Henrici metric of non‐normality as indices of transient dynamics. I found that balancing profoundly changes the picture of which populations have the greatest or least potential transient dynamics. Using a population projection matrix for northern pike (Esox lucius), I demonstrate how balancing influences pseudospectra contour plots that are used to infer transient dynamics.