Time Step Research Articles

On the Generalization of Learned Constraints for ASP Solving in Temporal Domains

Abstract The representation of a temporal problem in answer set programming (ASP) usually boils down to using copies of variables and constraints, one for each time stamp, no matter whether it is directly encoded or expressed via an action or temporal language. The multiplication of variables and constraints is commonly done during grounding, and the solver is completely ignorant about the temporal relationship among the different instances. On the other hand, a key factor in the performance of today’s ASP solvers is conflict-driven constraint learning. Our question in this paper is whether a constraint learned for particular time steps can be generalized and reused at other time steps, and ultimately whether this enhances the overall solver performance on temporal problems. Knowing well the domain of time, we study conditions under which learned dynamic constraints can be generalized. Notably, we identify a property of temporal representations that enables the generalization of learned constraints across all time steps. It turns out that most ASP planning encodings either satisfy this property or can be easily adapted to do so. In addition, we propose a general translation that transforms programs to fulfill this property. Finally, we empirically evaluate the impact of adding the generalized constraints to an ASP solver.

Marine species and assemblage change foreshadowed by their thermal bias over Early Jurassic warming

A mismatch of species’ thermal preferences to their environment may indicate how they will respond to future climate change. Averaging this mismatch across species may forewarn that some assemblages will undergo greater reorganization, extirpation, and possibly extinction, than others. Here, we examine how regional warming determines species occupancy and assemblage composition of marine bivalves, brachiopods, and gastropods over one-million-year time steps during the Early Jurassic. Thermal bias, the difference between modelled regional temperatures and species’ long-term thermal optima, predicts a gradient of species occupancy response to warming. Species that become extirpated or extinct tend to have cooler temperature preferences than immigrating species, while regionally persisting species fell midway. Larger regional changes in summer seawater temperatures (up to +10 °C) strengthen the relationship between species thermal bias and the response gradient, which is also stronger for brachiopods than for bivalves, while the relationship collapses during severe seawater deoxygenation. At +3 °C regional seawater warming, around 5 % of pre-existing benthic species in a regional assemblage are extirpated, and immigrating species comprise around one-fourth of the new assemblage. Our results validate thermal bias as an indicator of immigration, persistence, extirpation, and extinction of marine benthic species and assemblages under modern-like magnitudes of climate change.

A Parallel Algorithm of Stochastic Model Predictive Control by Partial Minimization

ABSTRACTThis article proposes a parallel algorithm of stochastic model predictive control (SMPC) for linear discrete‐time systems. The proposed algorithm uses multiple threads to solve respective optimization problems at different time steps in parallel, without inter‐thread communication during each optimization. Each thread sequentially solves a stochastic optimal control problem (SOCP) for optimizing closed‐loop performance against future disturbances and a partial minimization problem for optimizing a subset of decision variables of the SOCP. The partial minimization problem computes the control input according to the last measured state to satisfy chance constraints and can be solved much faster than the original SOCP. Consequently, the proposed algorithm can reduce the implementable minimum sampling period compared to the original SMPC. A numerical example of controlling room temperature showed that the proposed algorithm achieves control performance almost identical to that of closed‐loop SMPC, which optimizes closed‐loop performance. However, the implementable minimum sampling period of the proposed algorithm is much shorter than that of the closed‐loop SMPC, even with parallelization overhead.

Predicting nonequilibrium Green’s function dynamics and photoemission spectra via nonlinear integral operator learning

Abstract Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of large-scale nonequilibrium phenomena in realistic materials face serious challenges due to intrinsic high-dimensionality of quantum many-body problems and the absence of time-invariance. The nonequilibrium properties of many-body systems can be described by the dynamics of the correlator, or the Green’s function of the system, whose time evolution is given by a high-dimensional system of integro-differential equations, known as the Kadanoff–Baym equations (KBEs). The time-convolution term in KBEs, which needs to be recalculated at each time step, makes it difficult to perform long-time numerical simulation. In this paper, we develop an operator-learning framework based on recurrent neural networks (RNNs) to address this challenge. We utilize RNNs to learn the nonlinear mapping between Green’s functions and convolution integrals in KBEs. By using the learned operators as a surrogate model in the KBE solver, we obtain a general machine-learning scheme for predicting the dynamics of nonequilibrium Green’s functions. Besides significant savings per each time step, the new methodology reduces the temporal computational complexity from O ( N t 3 ) to O ( N t ) where Nt is the number of steps taken in a simulation, thereby making it possible to study large many-body problems which are currently infeasible with conventional KBE solvers. Through various numerical examples, we demonstrate the effectiveness of the operator-learning based approach in providing accurate predictions of physical observables such as the reduced density matrix and time-resolved photoemission spectra. Moreover, our framework exhibits clear numerical convergence and can be easily parallelized, thereby facilitating many possible further developments and applications.

Reduced-order modeling for complex 3D seismic wave propagation

Summary Elastodynamic Green’s functions are an essential ingredient in seismology as they form the connection between direct observations of seismic waves and the earthquake source. They are also fundamental to various seismological techniques including physics-based ground motion prediction and kinematic or dynamic source inversions. In regions with established 3D models of the Earth’s elastic structure, such as southern California, 3D Green’s functions can be computed using numerical simulations of seismic wave propagation. However, such simulations are computationally expensive which poses challenges for real-time ground motion prediction and uncertainty quantification in source inversions. In this study, we address these challenges by using a reduced-order model (ROM) approach that enables the rapid evaluation of approximate Green’s functions. The ROM technique developed approximates three-component time-dependent surface velocity wavefields obtained from numerical simulations of seismic wave propagation. We apply our ROM approach to a 50 km × 40 km area in greater Los Angeles accounting for topography, site effects, 3D subsurface velocity structure, and viscoelastic attenuation. The ROM constructed for this region enables rapid computation (≈0.0001 CPU hours) of complete, high-resolution (500 m spacing), 0.5 Hz surface velocity wavefields that are accurate for a shortest wavelength of 1.0 km for a single elementary moment tensor source. Using leave-one-out cross validation, we measure the accuracy of our Green’s functions for the CVM-S velocity model in both the time domain and frequency domain. Averaged across all sources, receivers, and time steps, the error in the rapid seismograms is less than 0.01 cm/s. We demonstrate that the ROM can accurately and rapidly reproduce simulated seismograms for generalized moment tensor sources in our region, as well as kinematic sources by using a finite fault model of the 1987 MW 5.9 Whittier Narrows earthquake as an example. We envision that rapid, accurate Green’s functions from reduced-order modeling for complex 3D seismic wave propagation simulations will be useful for constructing real-time ground motion synthetics and source inversions with high spatial resolution.

Aero-engine remaining useful life prediction using a TCN prognostic model enhanced with dual-dimensional fusion attention

Abstract Remaining useful life (RUL) prediction is an essential technique in the prognostics and health management (PHM) of aero-engines, crucial for ensuring reliability and safety. Recently, data-driven methods have achieved notable progress in aero-engine RUL prediction. However, they often neglect the impact of dimensional information and the coupling information between dimensions, failing to meet the requirements of long-term prediction tasks for aero-engines. This paper presents a prognostic model for aero-engine RUL prediction, utilizing a temporal convolutional network (TCN) enhanced by dual-dimensional fusion attention to tackle these challenges. Initially, the feature attention (FA) module is employed to weight the data from various engine sensors, thereby emphasizing key features. Subsequently, the TCN learns the temporal dependencies from the weighted input data. Additionally, a dual-dimension fusion attention (DDFA) module is designed to account for interactions between different dimensional data of the engine. This module extracts features from various sensors and time steps through parallel sub-structures and captures the coupling information between dimensions using an attention fusion unit, achieving inter-dimensional correlation of aero-engine data. Finally, the proposed model’s effectiveness was verified using the widely recognized C-MAPSS dataset. The results demonstrate that it outperforms state-of-the-art methods in aero-engine RUL prediction accuracy, confirming its superiority.

CMADRL: Cross-Modal Attention Based Deep Reinforcement Learning for Mobile Robot’s Obstacle Avoidance

Abstract The multimodal perception is very crucial for mobile robots to achieve safe autonomous
steering in complex and changing environments without colliding with obstacles. In spite of the fact that a rich environmental information can be provided by the multimodal data, how to integrate the complementary features from different sources effectively remains an open issue. In this paper, a simple yet effective multimodal deep reinforcement learning (DRL) method, CMADRL, by fusing two input modalities such as depth images and pseudo-LiDAR data generated by RGB-D cameras, is proposed to improve the performance of single sensor in environmental perception tasks. And the Convolutional LSTM Network (ConvLSTM) layers are also adopted to extract spatiotemporal features and capture temporal relationships in consecutive time steps, which allow the robot to predict dynamic changes of the environment. In addition, A crossmodal fusion module is designed to optimize the multimodal data fusion scheme, with dynamic weighting and merging of features from different modalities, allowing the agent to focus more reasonably on the current state and improving the accuracy and efficiency of the obstacle avoidance strategy. The experimental results show that the proposed approach achieved significant performance in cumulative rewards, convergence speed, and success rate. Additionally, tests in both simulated and real-world environments further verify that collisions are effectively avoided using only a low-cost RGB-D camera, demonstrating the method’s strong generalization capabilities.

Modeling Lake Titicaca's water balance: the dominant roles of precipitation and evaporation

Abstract. In the face of climate change and increasing anthropogenic pressures, a reliable water balance is crucial for understanding the drivers of water level fluctuations in large lakes. However, in poorly gauged hydrosystems such as Lake Titicaca, most components of the water balance are not measured directly. Previous estimates for this lake have relied on scaling factors to close the water balance, which introduces additional uncertainty. This study presents an integrated modeling framework based on conceptual models to quantify natural hydrological processes and net irrigation consumption. It was implemented in the Water Evaluation and Planning System (WEAP) platform at a daily time step for the period 1982–2016, considering the following terms of the water balance: upstream inflows, direct precipitation and evaporation over the lake, and downstream outflows. To estimate upstream inflows, we evaluated the impact of snow and ice processes and net irrigation withdrawals on predicted streamflow and lake water levels. We also evaluated the role of heat storage change in evaporation from the lake. The results showed that the proposed modeling framework makes it possible to simulate lake water levels ranging from 3808 to 3812 m a.s.l. with good accuracy (RMSE = 0.32 m d−1) over a wide range of long-term hydroclimatic conditions. The estimated water balance of Lake Titicaca shows that upstream inflows account for 56 % (958 mm yr−1) and direct precipitation over the lake for 44 % (744 mm yr−1) of the total inflows, while 93 % (1616 mm yr−1) of the total outflows are due to evaporation and the remaining 7 % (121 mm yr−1) to downstream outflows. The water balance closure has an error of −15 mm yr−1 without applying scaling factors. Snow and ice processes, together with net irrigation withdrawals, had a minimal impact on variations in the lake water level. Thus, Lake Titicaca is primarily driven by variations in precipitation and high evaporation rates. These results will be useful for supporting decision-making in water resource management. We demonstrate that a simple representation of hydrological processes and irrigation enables accurate simulation of water levels. The proposed modeling framework could be replicated in other poorly gauged large lakes because it is relatively easy to implement, requires few data, and is computationally inexpensive.

Impact of Annually Variable Dust Activity on the Recession of the Martian South Polar Seasonal Cap

Abstract Suspended dust is a vital component of Martian climatic system and its temporal-spatial variation can influence the recession of the South Polar Seasonal Cap (SPSC). However, dust activity varies across different stages and years, affecting the SPSC recession process differently. Continuous observations of SPSC/South Polar Residual Cap (SPRC) across several Martian years, alongside segmented analyses of annual dust activity, will provide new insights into the climate conditions of Martian south polar region. Here, we performed a combined analysis on the extents of SPSC from MY28-MY31 and MY36, together with the concurrent Martian atmospheric optical thickness, to assess the influence of dust activity at various recession time steps. Results show that dust activity peaks in both spring and summer can impact the SPSC/SPRC recession. The recession process is accelerated if the dust activity peak occurs earlier. If the timing of the peak dust activity is identical, the intensity of the dust activity influences the recession. Specific regions, such as the “Cryptic Region” and the Mountains of Mitchel, respond uniquely to dust activity. Higher dust intensity slows the recession of the Cryptic Region, while the SPSC in the Mountains of Mitchel area shows variability in recession timing based on local dust activity intensity. This research provides observational constraints that enhance our understanding of Martian atmospheric circulation and can potentially aid the future development of polar dust activity models.

Energy-preserving methods for gyrocenter system in strong magnetic field

Abstract We formulate second-order and fourth-order energy-preserving methods with two explicit corrections for gyrocenter system in a strong magnetic field 1 ϵ B ( X ) where the ∥ B ( X ) ∥ 2 = O ( 1 ) and ϵ < < 1. We theoretically show that the error bound of the two methods are independent of ϵ. The two explicit corrections are both manifold corrections. The first correction is confined to the manifold that the Hamiltonian at current time step should equal to the Hamiltonian at former time step and the second correction is confined to the manifold that the Hamiltonian at current time step should equal to the original Hamiltonian. Numerical experiments illustrate the impact of the ϵ on the phase orbit and the global error. Additionally, the numerical results show that the energy-preserving methods with the first correction show its advantage in long-term energy conservation than the energy-preserving methods without correction. The energy-preserving methods with the second correction behaves better in energy conservation than those with the first correction as the energy error of the former ones can be bounded by the machine precision over long time.

A Machine Learning Approach to Volume Tracking in Multiphase Flow Simulations

This work presents a machine learning (ML) approach to volume-tracking for computational simulations of multiphase flow. It is an alternative to a commonly used procedure in the volume-of-fluid (VOF) method for volume tracking, in which the phase interfaces are reconstructed for flux calculation followed by volume advection. Bypassing the computationally expensive steps of interface reconstruction and flux calculation, the proposed ML approach performs volume advection in a single step, directly predicting the volume fractions at the next time step. The proposed ML function is two-dimensional and has eleven inputs. It was trained using MATLAB’s (R2021a) Deep Learning Toolbox with a grid search method to find an optimal neural network configuration. The performance of the ML function is assessed using canonical test cases, including translation, rotation, and vortex tests. The errors in the volume fraction fields obtained by the ML function are compared with those of the VOF method. In ideal conditions, the ML function speeds up the computations four times compared to the VOF method. However, in terms of overall robustness and accuracy, the VOF method remains superior. This study demonstrates the potential of applying ML methods to multiphase flow simulations while highlighting areas for further improvement.

Computational Approaches to Compressible Micropolar Fluid Flow in Moving Parallel Plate Configurations

In this paper, we consider the unsteady flow of a compressible micropolar fluid between two moving, thermally isolated parallel plates. The fluid is characterized as viscous and thermally conductive, with polytropic thermodynamic properties. Although the mathematical model is inherently three-dimensional, we assume that the variables depend on only a single spatial dimension, reducing the problem to a one-dimensional formulation. The non-homogeneous boundary conditions representing the movement of the plates lead to moving domain boundaries. The model is formulated in mass Lagrangian coordinates, which leads to a time-invariant domain. This work focuses on numerical simulations of the fluid flow for different configurations. Two computational approaches are used and compared. The first is based on the finite difference method and the second is based on the Faedo–Galerkin method. To apply the Faedo–Galerkin method, the boundary conditions must first be homogenized and the model equations reformulated. On the other hand, in the finite difference method, the non-homogeneous boundary conditions are implemented directly, which reduces the computational complexity of the numerical scheme. In the performed numerical experiments, it was observed that, for the same accuracy, the Faedo–Galerkin method was approximately 40 times more computationally expensive compared to the finite difference method. However, on a dense numerical grid, the finite difference method required a very small time step, which could lead to an accumulation of round-off errors. On the other hand, the Faedo–Galerkin method showed the convergence of the solutions as the number of expansion terms increased, despite the higher computational cost. Comparisons of the obtained results show good agreement between the two approaches, which confirms the consistency and validity of the numerical solutions.

Coupled dynamic analysis of moored floating structures by a hybrid Laplace-time domain method

The coupled dynamic analysis of moored floating structures has often been conducted in the time domain by iteratively solving the Cummins equation, treating the mooring effects as an additional nonlinear load. However, the time domain (TD) method requires performing a convolution integral at each time step, which is costly in computational time. This paper innovatively develops an efficient hybrid Laplace-time domain method (HLTD) on implementing the coupled dynamic analysis of moored floating structures. The proposed method divides the external load into a number of segments and models the mooring system by the catenary theory. Under each segment, while the iterative operations used in the TD method is borrowed to handle the coupled behavior, the HLTD method computes the motions of the floating structure under each iteration by the pole-residue operations in the Laplace domain (LD). As the complicated convolutional integral computation required in the TD method is replaced by simple algebraic pole-residue calculations in the complex plane, the HLTD method is more efficient. Additionally, the HLTD method derives analytical response solutions for the moored floating system. Its efficiency and accuracy are demonstrated by comparing with the TD method through a moored float-over barge to irregular waves.

Once Upon a Time Step: A Closed-Loop Approach to Robust MPC Design

Once Upon a Time Step: A Closed-Loop Approach to Robust MPC Design

Incorporating memory into propagation of 1-electron reduced density matrices

For any linear system with unreduced dynamics governed by invertible propagators, we derive a closed, time-delayed, linear system for a reduced-dimensional quantity of interest. This method does not target dimensionality reduction: rather, this method helps shed light on the memory-dependence of 1-electron reduced density matrices in time-dependent configuration interaction (TDCI), a scheme to solve for the correlated dynamics of electrons in molecules. Though time-dependent density functional theory has established that the 1-electron reduced density possesses memory-dependence, the precise nature of this memory-dependence has not been understood. We derive a symmetry/constraint-preserving method to propagate reduced TDCI electron density matrices. In numerical tests on two model systems (H2 and HeH+), we show that with sufficiently large time-delay (or memory-dependence), our method propagates reduced TDCI density matrices with high quantitative accuracy. We study the dependence of our results on time step and basis set. To implement our method, we derive the 4-index tensor that relates reduced and full TDCI density matrices. Our derivation applies to any TDCI system, regardless of basis set, number of electrons, or choice of Slater determinants in the wave function.

Numerical simulation method of multi-fracture fracturing coupling proppant transport

Hydraulic fracturing is a critical technology for the efficient development of unconventional reservoirs. It involves multi-physics coupling, making its numerical simulation an extremely challenging task. In this paper, an efficient hydraulic fracturing simulator is developed by integrating a simplified proppant transport model into the multi-fracture fracturing framework. In the fracture propagation model, the finite volume method is used to solve fluid flow, while the displacement discontinuity method is employed rock deformation. Proppant transport is realized by the simplified Eulerian–Eulerian method, which only needs to consider the one-dimensional fluid flow. The high-precision weighted essentially non-oscillatory scheme is used to solve the nonlinear proppant transport equation. Compared with the Eulerian–Lagrangian method, the proposed method enhances simulation efficiency by 2–3 orders of magnitude. The numerical model is verified through physical experiments and fracture analytical solutions. The fracture propagation and proppant transport models are implemented via a unidirectional coupling strategy. First, the fully coupled model calculates the fracture morphology, followed by the computation of proppant distribution at each time step. Four cases were established to analyze the effects of fracturing fluid injection time, injection rate, fracture cluster spacing, and the number of fracture clusters on the industrial-scale proppant distribution in fractures. This method can be applied to large-scale fracturing simulation, optimization of fracturing parameters and other fields requiring high computational efficiency.

Spatio-temporal transformers for decoding neural movement control

Objective. Deep learning tools applied to high-resolution neurophysiological data have significantly progressed, offering enhanced decoding, real-time processing, and readability for practical applications. However, the design of artificial neural networks to analyze neural activityin vivoremains a challenge, requiring a delicate balance between efficiency in low-data regimes and the interpretability of the results.Approach. To address this challenge, we introduce a novel specialized transformer architecture to analyze single-neuron spiking activity. The model is tested on multi-electrode recordings from the dorsal premotor cortex of non-human primates performing a motor inhibition task.Main results. The proposed architecture provides an early prediction of the correct movement direction, achieving accurate results no later than 230 ms after the Go signal presentation across animals. Additionally, the model can forecast whether the movement will be generated or withheld before a stop signal, unattended, is actually presented. To further understand the internal dynamics of the model, we compute the predicted correlations between time steps and between neurons at successive layers of the architecture, with the evolution of these correlations mirrors findings from previous theoretical analyses.Significance. Overall, our framework provides a comprehensive use case for the practical implementation of deep learning tools in motor control research, highlighting both the predictive capabilities and interpretability of the proposed architecture.

A fast method based on variable time steps for 2D nonlinear time-fractional generalized Benjamin–Bona–Mahony–Burgers equation: Error and stability analysis

A fast method based on variable time steps for 2D nonlinear time-fractional generalized Benjamin–Bona–Mahony–Burgers equation: Error and stability analysis

Projected Wave Function Extrapolation Scheme to Accelerate Plane-Wave Hybrid Functional-Based Born-Oppenheimer Molecular Dynamics Simulations.

Born-Oppenheimer molecular dynamics (BOMD) simulations are of great interest for the dynamic properties of molecular and solid systems. However, BOMD simulations necessitate not only an extensive period of dynamical evolution but also costly self-consistent-field (SCF) electronic structure calculations, especially for hybrid functional-based BOMD (H-BOMD) simulations within plane-wave basis sets. Here, we propose an improved always stable predictor-corrector (ASPC) method for the wave function extrapolation to accelerate the plane-wave H-BOMD simulations, named projected ASPC (PASPC), yielding a wave function closer to the actual solution space and efficiently reducing the number of SCF iterations at each MD step. We investigated the convergence properties of different extrapolation schemes for molecular and solid systems. Numerical results demonstrate that plane-wave H-BOMD simulations can be significantly faster than conventional cases by combining the accelerated algorithms with the PASPC method. The energy drift is also evaluated, showing that PASPC produces energy drift with smaller oscillations and can simulate a larger time step for systems containing heavy atoms, demonstrating the accuracy of the extrapolation schemes. Furthermore, H-BOMD simulations showcase more accurate power and infrared spectra of silicon dioxide and liquid water that are comparable to those of experimental measurements.

HERA: a high-resolution pan-European hydrological reanalysis (1951–2020)

Abstract. Since 1950, anthropogenic activities have altered the climate, land cover, soil properties, channel morphologies, and water management in the river basins of Europe. This has resulted in significant changes in hydrological conditions. The availability of consistent estimates of river flow at the global and continental levels is a necessity for assessing changes in the hydrological cycle. To overcome limitations posed by observations (incomplete records, inhomogeneous spatial coverage), we simulate river discharge for Europe for the period 1951–2020 using a state-of-the-art hydrological modelling approach. We use the new European set-up of the OS LISFLOOD model, running at 1 arcmin (≈1.8 km) with 6-hourly time steps. The hydrological model is forced by climate reanalysis data (ERA5-Land) that are bias-corrected and downscaled to the model resolution with gridded weather observations. The model also incorporates 72 surface field maps representing catchment morphology, vegetation, soil properties, land use, water demand, lakes, and reservoirs. Inputs related to human activities are evolving through time to emulate societal changes. The resulting Hydrological European ReAnalysis (HERA) provides 6-hourly river discharge for 282 521 river pixels with an upstream area >100 km2. We assess its skill using 2448 river gauging stations distributed across Europe. Overall, HERA delivers satisfying results (median KGE′=0.55), despite a general underestimation of observed mean discharges (mean bias=-13.1 %), and demonstrates a capacity to reproduce statistics of observed extreme flows. The performance of HERA increases through time and with catchment size, and it varies in space depending on reservoir influence and model calibration. The fine spatial and temporal resolution results in an enhanced performance compared to previous hydrological reanalysis based on OS LISFLOOD for small- to medium-scale catchments (100–10 000 km2). HERA is the first publicly available long-term, high-resolution hydrological reanalysis for Europe. Despite its limitations, HERA enables the analysis of hydrological dynamics related to extremes, human influences, and climate change at a continental scale while maintaining local relevance. It also creates the opportunity to study these dynamics in ungauged catchments across Europe. The HERA hydrological reanalysis and its climate and dynamic socio-economic inputs are available via the JRC data catalogue: https://doi.org/10.2905/a605a675-9444-4017-8b34-d66be5b18c95 (Tilloy et al., 2024).