Configuration Space Research Articles

Physical reservoir computing: a tutorial

AbstractThis tutorial covers physical reservoir computing from a computer science perspective. It first defines what it means for a physical system to compute, rather than merely evolve under the laws of physics. It describes the underlying computational model, the Echo State Network (ESN), and also some variants designed to make physical implementation easier. It explains why the ESN model is particularly suitable for direct physical implementation. It then discusses the issues around choosing a suitable material substrate, and interfacing the inputs and outputs. It describes how to characterise a physical reservoir in terms of benchmark tasks, and task-independent measures. It covers optimising configuration parameters, exploring the space of potential configurations, and simulating the physical reservoir. It ends with a look at the future of physical reservoir computing as devices get more powerful, and are integrated into larger systems.

Tutorial on Molecular Latent Space Simulators (LSSs): Spatially and Temporally Continuous Data-Driven Surrogate Dynamical Models of Molecular Systems.

The inherently serial nature and requirement for short integration time steps in the numerical integration of molecular dynamics (MD) calculations place strong limitations on the accessible simulation time scales and statistical uncertainties in sampling slowly relaxing dynamical modes and rare events. Molecular latent space simulators (LSSs) are a data-driven approach to learning a surrogate dynamical model of the molecular system from modest MD training trajectories that can generate synthetic trajectories at a fraction of the computational cost. The training data may comprise single long trajectories or multiple short, discontinuous trajectories collected over, for example, distributed computing resources. Provided the training data provide sufficient sampling of the relevant thermodynamic states and dynamical transitions to robustly learn the underlying microscopic propagator, an LSS furnishes a global model of the dynamics capable of producing temporally and spatially continuous molecular trajectories. Trained LSS models have produced simulation trajectories at up to 6 orders of magnitude lower cost than standard MD to enable dense sampling of molecular phase space and large reduction of the statistical errors in structural, thermodynamic, and kinetic observables. The LSS employs three deep learning architectures to solve three independent learning problems over the training data: (i) an encoding of the high-dimensional MD into a low-dimensional slow latent space using state-free reversible VAMPnets (SRVs), (ii) a propagator of the microscopic dynamics within the low-dimensional latent space using mixture density networks (MDNs), and (iii) a generative decoding of the low-dimensional latent coordinates back to the original high-dimensional molecular configuration space using conditional Wasserstein generative adversarial networks (cWGANs) or denoising diffusion probability models (DDPMs). In this software tutorial, we introduce the mathematical and numerical background and theory of LSS and present example applications of a user-friendly Python package software implementation to alanine dipeptide and a 28-residue beta-beta-alpha (BBA) protein within simple Google Colab notebooks.

Supergeometric quantum effective action

Supergeometric quantum field theories (SG-QFTs) are theories that go beyond the standard supersymmetric framework, since they allow for general scalar-fermion field transformations on the configuration space of a supermanifold, without requiring an equality between bosonic and fermionic degrees of freedom. After revisiting previous considerations, we extend them by calculating the one-loop effective action of minimal SG-QFTs that feature nonzero fermionic curvature in two and four spacetime dimensions. By employing an intuitive approach to the Schwinger–DeWitt heat-kernel technique and a novel field-space generalized Clifford algebra, we derive the ultraviolet structure of characteristic effective-field-theory (EFT) operators up to four spacetime derivatives that emerge at the one-loop order and are of physical interest. Upon minimizing the impact of potential ambiguities due to the so-called multiplicative anomalies, we find that the EFT interactions resulting from the one-loop supergeometric effective action are manifestly diffeomorphically invariant in configuration space. The extension of our approach to evaluating higher loops of the supergeometric quantum effective action is described. The emerging landscape of theoretical and phenomenological directions for further research of SG-QFTs is discussed. Published by the American Physical Society 2024

Machine-Learning-Assisted Screening of Nanocluster Electrocatalysts: Mapping and Reshaping the Activity Volcano for the Oxygen Reduction Reaction.

In computational heterogeneous catalysis, Sabatier's principle-based activity volcano plots provide an intuitive guide to catalyst design but impose a fundamental constraint on the maximum achievable catalytic performance. Recently, subnano clusters have emerged as an exciting platform, offering high noble metal utilization and superior performance for various reactions compared to extended surfaces, reflecting a complex structure-activity relationship in the non-scalable regime. However, understanding their non-monotonic catalytic activity, attributed to the large configurational space and their fluxional identity, poses a formidable challenge. Here, we present a machine learning (ML) framework that captures the non-monotonic trends in oxygen reduction reaction (ORR) activity at the subnanometer scale, attributed to their dynamic fluxional characteristics. We demonstrate a size-dependent shifting and reshaping of the ORR activity volcano, with Au replacing Pt at the peak. Leveraging only upon the non-ab initio geometric and electronic properties, our trained ML model accurately captures the site-specific adsorption energies of intermediates at the subnanometer regime. To account for the inconsistent trend in activity, we analyzed the correlation between electronic and geometric properties. Our findings reveal that the d-filling and coupling matrix of the neighboring metal atom significantly influences the intermediate adsorption on the local chemical environment compared to the d-band center. Following this analysis, we utilized ML to map the catalyst distribution in the activity volcano and identified the five best sub-nano electrocatalysts, demonstrating overpotential values lower than or comparable to the Pt(111) surface for the ORR. This study provides intuitive guidelines for the rational designing of highly efficient electrocatalysts for fuel cell applications while modifying the activity volcano plots for electrocatalysts at the subnanometer regime.

An objective isogeometric mixed finite element formulation for nonlinear elastodynamic beams with incompatible warping strains

AbstractWe present a stable mixed isogeometric finite element formulation for geometrically and materially nonlinear beams in transient elastodynamics, where a Cosserat beam formulation with extensible directors is used. The extensible directors yield a linear configuration space incorporating constant in-plane cross-sectional strains. Higher-order (incompatible) strains are introduced to correct stiffness, whose additional degrees of freedom are eliminated by an element-wise condensation. Further, the present discretization of the initial director field leads to the objectivity of approximated strain measures, regardless of the degree of basis functions. For physical stress resultants and strains, we employ a global patch-wise approximation using B-spline basis functions, whose higher-order continuity enables using much fewer degrees of freedom than an element-wise approximation. For time-stepping, we employ implicit energy–momentum consistent scheme, which exhibits superior numerical stability in comparison to standard trapezoidal and mid-point rules. Several numerical examples are presented to verify the present method.

Robust and Adaptive Control of a Soft Continuum Manipulator for Minimally Invasive Surgery

This article investigates the model-based control in configurations space of a soft continuum manipulator for minimally invasive surgery. The main control challenges for these types of systems are the presence of model uncertainties and nonlinearities. To this end, a sliding-mode controller, a Lyapunov redesign controller, and an adaptive controller have been designed and compared by means of simulations and experiments on a prototype. The results indicate that the adaptive controller yields better accuracy but a slower transient. Conversely, the sliding-mode controller and Lyapunov redesign yield a faster response but can result in chattering or steady-state errors.

Challenges in Mathematics Arising from Theoretical and Computational Chemistry

The combination of theoretical chemistry and mathematics represents a significant advancement in science since it has yielded insights into the enigmas surrounding atoms and molecules. The advancement of technology has greatly benefited drug development, leading to significant advancements in both medicine and materials research. This summary discusses innovative methodologies and computational challenges in the expansive domain of theoretical and computational chemistry. Despite the computational challenges associated with the Schrodinger equation and Density Functional Theory (DFT), quantum mechanics offers a basic understanding of the behaviour of molecules and atoms. While MD simulations may not handle long-range interactions and complex configuration spaces, they nonetheless excel at capturing various time scales of molecular behaviour. Nevertheless, the process of transforming abstract notions into computer models for the purpose of solving MD simulations continues to be difficult; statistical mechanics offers a theoretical framework for understanding MD simulations. Data-driven methodologies and machine learning have significantly transformed the perspective of computational chemistry by enabling the observation and comprehension of very complex chemical interactions. We must also address concerns about interpretability, reliability in limited data streams, and system transferability. These challenges expedite the advancement of novel materials, product designs, and pharmaceuticals by leveraging machine learning and integrating it with specialised domain expertise. We used available data from many reputable databases, spanning the time period from 2010 to 2024. It is imperative to prioritise the advancement of multiscale modelling techniques and hybrid quantum-classical tools in order to achieve sufficient mastery over chemical phenomena. Another potential benefit is the use of novel mathematical models to uncover previously unknown patterns and connections in genetic data. The most effective way to tackle mathematical problems is by employing a straightforward approach and engaging in collaboration with experts from other fields. By adopting this approach, we can effectively address significant societal issues and propel advancements in chemistry. Keywords: mathematics, computational, chemistry, theoretical, challenges, quantum mechanics

Block-Correlated Coupled Cluster Theory Based on the Generalized Valence Bond Reference for Singlet-Triplet Energy Gaps of Strongly Correlated Systems.

A block-correlated coupled cluster (BCCC) method based on the triplet generalized valence bond (GVB) wave function (GVB-BCCC) has been implemented for the first time. By introducing several techniques, we have developed a practical and efficient GVB-BCCC code. The GVB-BCCC3 method (with up to three-pair correlation) can be used to deal with strongly correlated (SC) systems with triplet or singlet ground states, allowing singlet-triplet (S-T) energy gaps in the active space of SC systems computationally available. For selected SC systems, our calculations show that GVB-BCCC3 can always provide correct ground-state spin multiplicity as the complete active space configuration interaction (CASCI) or density matrix renormalization group (DMRG). Furthermore, we found that the S-T energy gaps from GVB-BCCC3 are quite consistent with CASCI or DMRG results. This work demonstrates that GVB-BCCC3 is a promising theoretical tool for describing S-T energy gaps within the active space of SC systems with large active spaces.

Probing phase transitions with correlations in configuration space

Probing phase transitions with correlations in configuration space

An actuator space optimal kinematic path tracking framework for tendon-driven continuum robots: Theory, algorithm and validation

Path tracking of continuum robots is a fundamental and crucial problem across various applications. In this article, we address this problem by focussing on three aspects. Firstly, we propose an efficient multi-solution inverse kinematics solver for three-section constant curvature robots by bridging the theoretical reduction and the numerical correction. Secondly, we derive a linear tendon-driven actuation model, establishing the connection between the robot configuration space and the actuator space. With this model, we achieve optimal distance planning and optimal time allocation considering the constraints of actuator velocity and acceleration, generating a continuous trajectory directly in the actuator space. Finally, we present our kinematic path tracking framework, which includes offline optimal trajectory planning and online feedforward and feedback control. Experiments are conducted both in simulations and in the real world on our three-section tendon-driven continuum robot. The experiments validate the increased efficiency, higher success rates, and accessibility of multiple solutions offered by our inverse kinematics solver, as well as the optimality in distance planning and time allocation in the actuator space. Performance improvements in tracking accuracy are demonstrated through comparative experiments and the application of our framework in path tracking tasks with obstacles is presented through a case study.

Effects of Tree Spacing and Branch Configuration on Production, Fruit Quality, and Leaf Minerals of ‘Aztec Fuji’ Apple Trees in a Tatura Trellis System Over 5 Years

Tree spacing and branch architecture are critical for the productivity of high-density orchards. The influence of two tree spacings of 45.7 cm × 366 cm and 91.4 cm × 366 cm each with two branch architectures or configurations of shortened branch (ShBr) or overlapped branch (OverBr) on tree growth, yield components, fruit quality, and leaf mineral nutrients in an ‘Aztec Fuji’ apple (Malus domestica Borkh.) orchard with a 60-degree Tatura trellis (V) system was studied over 5 years. Trees planted with 91.4-cm spacing had a significantly greater trunk cross-sectional area (TCSA), higher number of fruit and greater yield per tree, and greater cumulative yield efficiency than those of trees planted with 45.7-cm spacing during 2012–16. Tree spacing did not significantly affect fruit weight and firmness at harvest or after storage. However, trees planted with 91.4-cm spacing always had higher fruit color, sunburn, fruit russet, and watercore at harvest and a higher soluble solids concentration but lower fruit bitter pit at harvest and after storage compared to those of trees with 45.7-cm spacing. These differences were often significant. Trees with 45.7-cm spacing had significantly higher leaf concentrations of potassium, iron, copper, and manganese and relatively higher leaf zinc than those of trees with 91.4-cm spacing. Trees trained according to ShBr architectures had a relatively larger TCSA than those of trees with an OverBr configuration every year. Branching architectures did not affect the number of fruits per tree, yield per tree, yield per hectare, yield efficiency, or biennial bearing index in any year. Trees with a ShBr architecture had significantly larger fruits than those with an OverBr system every year and over the 5 years. Trees with a ShBr architecture had higher average leaf fresh and dry weights and calcium concentration but a similar percentage of dry weight compared to those of trees with an OverBr architecture.

A Large Atomic Partition Model for Materials Discovery

Accurate and efficient prediction of benchmark properties is essential to the discovery of diverse functional materials, but searching vast element combinatorial and bonding configurational spaces presents formidable challenges to current computational techniques. Here, we devise a large atomic partition (LAP) model featuring a scheme to partition material properties into constituent atomic attributes, which are validated by a data-driven calibration procedure and assigned to elements across the periodic table, then utilized as raw ingredients to assemble and assess targeted properties of new materials. Distinct subtypes are designated for each element based on local atomic environments such as coordination number and valence state, and the parameter count of the LAP model can be tuned widely to tailor prediction accuracy and computational efficiency. As demonstrative case studies, we explore volumetric cohesive energy, bulk modulus, and shear modulus, and the results showcase superior accuracy, efficiency, universality, and interpretability of the LAP model compared to alternative approaches. Moreover, based on the predicted elastic moduli, we discovered a series of rare and highly sought-after compounds exhibiting concurrent superior hardness and toughness, highlighting the promise of the LAP model in high-throughput screening for advanced materials with targeted outstanding functionalities.

Hamiltonian integrable systems in a magnetic field and symplectic-Haantjes geometry

We investigate the geometry of classical Hamiltonian systems immersed in a magnetic field in three-dimensional (3D) Riemannian configuration spaces. We prove that these systems admit non-trivial symplectic-Haantjes manifolds, which are symplectic manifolds endowed with an algebra of Haantjes (1,1)-tensors. These geometric structures allow us to determine separation variables for known systems algorithmically. In addition, the underlying Stäckel geometry is used to construct new families of integrable Hamiltonian models immersed in a magnetic field.

Piecewise Omnigenous Stellarators.

In omnigenous magnetic fields, charged particles are perfectly confined in the absence of collisions and turbulence. For this reason, the magnetic configuration is optimized to be close to omnigenity in any candidate for a stellarator fusion reactor. However, approaching omnigenity imposes severe constraints on the spatial variation of the magnetic field. In particular, the topology of the contours of constant magnetic field strength on each magnetic surface must be such that there are no particles transitioning between different types of wells. This, in turn, usually leads to complicated plasma shapes and coils. This Letter presents a new family of optimized fields that display tokamak-like collisional energy transport while having transitioning particles. This result radically broadens the space of accessible reactor-relevant configurations.

The Geography of Inequality: Socio-Spatial Segregation and Climate Vulnerability in Brazilian Urban Peripheries

This article elaborates on the relationship between socio-spatial segregation and climate vulnerability in urban peripheries, pointing out how the structural inequalities of cities are further deepened by climate change processes. The paper critically engages with the core question: How does urban planning, and its public policies fall short of protecting marginalized populations while prioritizing more central and valued areas? This research rests on a critical review of literature, referring to the theories of Henri Lefebvre, David Harvey, Flavio Villaça, Roberto Lobato Corrêa, Milton Santos, and Mike Davis. Their theories on the unequal production of urban space and the exclusion of poor populations are crucial for understanding data on the effects of climate change on Brazilian urban peripheries. The adopted methodology explores intersections between spatial segregation and climatic vulnerability, highlighting how the neoliberal model of urbanization deepens the exposure of peripheries to environmental risks. The research establishes the urgency of rethinking urban policies as the intensity of extreme weather events increases, suggesting fair solutions to promote climate justice. The study's findings indicate that the current configuration of urban space not only intensifies the marginalization of peripheries but also amplifies their vulnerability to climate crises. This underscores the need for urban planning that fairly redistributes investments and resources, prioritizing the most vulnerable areas and promoting socio-spatial inclusion.

Effect of sowing methods, spacings, and fertilizer levels on quantitative and qualitative traits and economics of brown top millet (Brachiaria ramosa L.) under different cropping seasons

A field study was conducted during the Summer, Kharif, and Rabi seasons of 2023-2024 to evaluate brown top millet under two sowing methods (direct sowing and transplantation), three spacing configurations (20 x 10, 30 x 10 and 45 x 10 cm), and three fertilizer doses (75% of the recommended dose of fertilizer (RDF) (45:20:15 kg ha-1), 100% RDF (60:30:20 kg ha-1), and 125% RDF (75:40:25 kg ha-1)). The study was designed as a factorial randomized complete block design assessing growth, yield, thiamine content, and economics. The results indicated that the summer season was more favorable for growth than the Kharif and Rabi seasons. Direct sown crops (E1) exhibited significantly higher growth attributes, yield, and economics than transplanted crops (E2). The spacing configuration of 45 x 10 cm (S3) recorded significantly superior growth and yield parameters compared to 20 x 10 cm (S1). Applying 125% RDF (N3) resulted in significantly enhanced growth, yield, quality, and economic return compared to 75% RDF. Among the interactions, the combination of direct sown with narrow spacing and 125% RDF (E1 x S1 x N3) led to significantly higher growth parameters. In comparison, the combination of direct sowing with wider spacing and 125% RDF (E1 x S3 x N3) resulted in higher grain yields (2005, 1759, 1548 kg ha-1) and benefit-cost ratios (2.64, 2.58, and 2.58) across the same seasons. However, the differences in grain yield among the treatment combinations were statistically non-significant. These findings provide a valuable foundation for future research and agricultural practices aimed at maximizing the potential of brown top millet.

Shannon Wavelet‐Based Approximation Scheme for Information Entropy Integrals in Confined Domain

ABSTRACTIn this work, the author attempted to develop a Shannon wavelet‐based numerical scheme to approximate the information entropies in both configuration and momentum space corresponding to the ground and adjacent excited energy states of one‐dimensional Schrödinger equation appearing in non‐relativistic quantum mechanics. The development of this scheme is based on the judicious use of sinc scale functions as an approximation basis and a suitable numerical quadrature to approximate entropies in position and momentum spaces. Priori and posteriori errors appearing in the approximations of wave functions and entropy integrals have been discussed. The scheme (coded in Python) has been subsequently exercised for various exactly solvable and quasi‐exactly solvable non‐relativistic quantum mechanical models in confined domain.

Inferring Cosmological Parameters on SDSS via Domain-generalized Neural Networks and Light-cone Simulations

We present a proof-of-concept simulation-based inference on Ωm and σ 8 from the Sloan Digital Sky Survey (SDSS) Baryon Oscillation Spectroscopic Survey (BOSS) LOWZ Northern Galactic Cap (NGC) catalog using neural networks and domain generalization techniques without the need of summary statistics. Using rapid light-cone simulations L-picola, mock galaxy catalogs are produced that fully incorporate the observational effects. The collection of galaxies is fed as input to a point cloud-based network, Minkowski-PointNet . We also add relatively more accurate Gadget mocks to obtain robust and generalizable neural networks. By explicitly learning the representations that reduce the discrepancies between the two different data sets via the semantic alignment loss term, we show that the latent space configuration aligns into a single plane in which the two cosmological parameters form clear axes. Consequently, during inference, the SDSS BOSS LOWZ NGC catalog maps onto the plane, demonstrating effective generalization and improving prediction accuracy compared to non-generalized models. Results from the ensemble of 25 independently trained machines find Ωm = 0.339 ± 0.056 and σ 8 = 0.801 ± 0.061, inferred only from the distribution of galaxies in the light-cone slices without relying on any indirect summary statistics. A single machine that best adapts to the Gadget mocks yields a tighter prediction of Ωm = 0.282 ± 0.014 and σ 8 = 0.786 ± 0.036. We emphasize that adaptation across multiple domains can enhance the robustness of the neural networks in observational data.

Elucidating Protein Structures in the Gas Phase: Traversing Configuration Space with Biasing Methods.

Achieving accurate characterization of protein structures in the gas phase continues to be a formidable challenge. To tackle this issue, the present study employs Molecular Dynamics (MD) simulations in tandem with enhanced sampling techniques (methods designed to efficiently explore protein conformations). The objective is to identify suitable structures of proteins by contrasting their calculated Collision Cross-Section (CCS) with those observed experimentally. Significant discrepancies were observed between the initial MD-simulated and experimentally measured CCS values through Ion Mobility-Mass Spectrometry (IMS-MS). To bridge this gap, we employed two distinct enhanced sampling methods, Harmonic Biasing Potential and Adaptive Biasing Force, which help the proteins overcome energy barriers to adopt more compact configurations. These techniques leverage the radius of gyration as a reaction coordinate (guiding parameter), guiding the system toward compressed states that potentially match experimental configurations more closely. The guiding forces are only employed to overcome existing barriers and are removed to allow the protein to naturally arrive at a potential gas phase configuration. The results demonstrated close alignment (within ∼4%) between simulated and experimental CCS values despite using different strengths and/or methods, validating their efficacy. This work lays the groundwork for future studies aimed at optimizing biasing methods and expanding the collective variables used for more accurate gas-phase structural predictions.

Comparison of Matrix Product State and Multiconfiguration Time-Dependent Hartree Methods for Nonadiabatic Dynamics of Exciton Dissociation.

The excited-state dynamics of organic molecules, molecular aggregates, and donor-acceptor clusters is typically governed by the interplay of electronic excitations and, due to their flexibility and soft bonding, by the interaction with their vibrations. This interaction in these systems can be characterized by a few relevant electronic states that are coupled to numerous vibrational normal modes, encompassing a vast configurational space of the molecules. The full quantum simulation of these type of systems has been long dominated by the multiconfiguration time-dependent Hartree (MCTDH) approach and its multilayer variants, which are considered the gold standard in the presence of electron-vibration coupling with a large number of modes. Recently, also the matrix product state ansatz (MPS) with appropriate time-evolution schemes has been applied to these types of Hamiltonians. In this article, we provide a numerical comparison of excited-state dynamics between the MCTDH and MPS approaches for two electron-vibration coupled systems. Notably, we consider two models for exciton dissociation at a P3HT:PCBM heterojunction, comprising two electronic states and 100 vibrational modes, and 26 electronic states and 113 vibrational modes, respectively. While both methods agree very well for the first model, more pronounced deviations are found for the second model. We trace back the divergence between the methods to the different way entanglement is treated.