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At least 649 records · Page 36

Parametric Finite Element Analysis of Naturally Corroded Steel Specimens Using 3D Surface Laser Scans

Corrosion is considered a uniform thickness reduction design guideline of the maritime industry. However, additionally, the corroded and irregular morphology of the surface affects the steel's load-bearing capacity and its impact on the strength and elongation behaviour of the steel is not yet fully understood. These effects on the local behaviour of steel structures under tensile loading were investigated with tensile tests on naturally corroded steel specimens and nonlinear finite element simulations including the corroded surface morphology with a uniform surface idealation. The models also include the deformed specimen shape. The developed approach led to highly accurate parametric finite element models predicting the ultimate tensile strength and longitudinal position of fracture. The results show that all included aspects are essential for accurate simulations, while solely the maximum available surface resolution was not as decisive.

corrosion↗

Attention-based quantum tomography

Abstract With rapid progress across platforms for quantum systems, the problem of many-body quantum state reconstruction for noisy quantum states becomes an important challenge. There has been a growing interest in approaching the problem of quantum state reconstruction using generative neural network models. Here we propose the ‘attention-based quantum tomography’ (AQT), a quantum state reconstruction using an attention mechanism-based generative network that learns the mixed state density matrix of a noisy quantum state. AQT is based on the model proposed in ‘Attention is all you need’ by Vaswani et al (2017 NIPS ) that is designed to learn long-range correlations in natural language sentences and thereby outperform previous natural language processing (NLP) models. We demonstrate not only that AQT outperforms earlier neural-network-based quantum state reconstruction on identical tasks but that AQT can accurately reconstruct the density matrix associated with a noisy quantum state experimentally realized in an IBMQ quantum computer. We speculate the success of the AQT stems from its ability to model quantum entanglement across the entire quantum system much as the attention model for NLP captures the correlations among words in a sentence.

97 MATHEMATICS AND COMPUTING↗

FINETUNA: fine-tuning accelerated molecular simulations

Abstract Progress towards the energy breakthroughs needed to combat climate change can be significantly accelerated through the efficient simulation of atomistic systems. However, simulation techniques based on first principles, such as density functional theory (DFT), are limited in their practical use due to their high computational expense. Machine learning approaches have the potential to approximate DFT in a computationally efficient manner, which could dramatically increase the impact of computational simulations on real-world problems. However, they are limited by their accuracy and the cost of generating labeled data. Here, we present an online active learning framework for accelerating the simulation of atomic systems efficiently and accurately by incorporating prior physical information learned by large-scale pre-trained graph neural network models from the Open Catalyst Project. Accelerating these simulations enables useful data to be generated more cheaply, allowing better models to be trained and more atomistic systems to be screened. We also present a method of comparing local optimization techniques on the basis of both their speed and accuracy. Experiments on 30 benchmark adsorbate-catalyst systems show that our method of transfer learning to incorporate prior information from pre-trained models accelerates simulations by reducing the number of DFT calculations by 91%, while meeting an accuracy threshold of 0.02 eV 93% of the time. Finally, we demonstrate a technique for leveraging the interactive functionality built in to Vienna ab initio Simulation Package (VASP) to efficiently compute single point calculations within our online active learning framework without the significant startup costs. This allows VASP to work in tandem with our framework while requiring 75% fewer self-consistent cycles than conventional single point calculations. The online active learning implementation, and examples using the VASP interactive code, are available in the open source FINETUNA package on Github.

97 MATHEMATICS AND COMPUTING↗

SYMBA: symbolic computation of squared amplitudes in high energy physics with machine learning

The cross section is one of the most important physical quantities in high-energy physics and the most time consuming to compute. While machine learning has proven to be highly successful in numerical calculations in high-energy physics, analytical calculations using machine learning are still in their infancy. In this work, we use a sequence-to-sequence model, specifically, a transformer, to compute a key element of the cross section calculation, namely, the squared amplitude of an interaction. We show that a transformer model is able to predict correctly 97.6% and 99% of squared amplitudes of quantum chromodynamics and quantum electrodynamics processes, respectively, at a speed that is up to orders of magnitude faster than current symbolic computation frameworks. We discuss the performance of the current model, its limitations and possible future directions for this work.

97 MATHEMATICS AND COMPUTING↗

Recipes for when physics fails: recovering robust learning of physics informed neural networks

Abstract Physics-informed neural networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be sensitive to errors in training data and overfit itself in dynamically propagating these errors over the domain of the solution of the PDE. It also shows how physical regularizations based on continuity criteria and conservation laws fail to address this issue and rather introduce problems of their own causing the deep network to converge to a physics-obeying local minimum instead of the global minimum. We introduce Gaussian process (GP) based smoothing that recovers the performance of a PINN and promises a robust architecture against noise/errors in measurements. Additionally, we illustrate an inexpensive method of quantifying the evolution of uncertainty based on the variance estimation of GPs on boundary data. Robust PINN performance is also shown to be achievable by choice of sparse sets of inducing points based on sparsely induced GPs. We demonstrate the performance of our proposed methods and compare the results from existing benchmark models in literature for time-dependent Schrödinger and Burgers’ equations.

97 MATHEMATICS AND COMPUTING↗

Infinite neural network quantum states: entanglement and training dynamics

We study infinite limits of neural network quantum states (∞-NNQS), which exhibit representation power through ensemble statistics, and also tractable gradient descent dynamics. Ensemble averages of entanglement entropies are expressed in terms of neural network correlators, and architectures that exhibit volume-law entanglement are presented. The analytic calculations of entanglement entropy bound are tractable because the ensemble statistics are simplified in the Gaussian process limit. A general framework is developed for studying the gradient descent dynamics of neural network quantum states (NNQS), using a quantum state neural tangent kernel (QS-NTK). For ∞-NNQS the training dynamics is simplified, since the QS-NTK becomes deterministic and constant. An analytic solution is derived for quantum state supervised learning, which allows an ∞-NNQS to recover any target wavefunction. Numerical experiments on finite and infinite NNQS in the transverse field Ising model and Fermi Hubbard model demonstrate excellent agreement with theory. ∞-NNQS opens up new opportunities for studying entanglement and training dynamics in other physics applications, such as in finding ground states.

quantum state supervised learning↗

A detailed study of interpretability of deep neural network based top taggers

Abstract Recent developments in the methods of explainable artificial intelligence (XAI) allow researchers to explore the inner workings of deep neural networks (DNNs), revealing crucial information about input–output relationships and realizing how data connects with machine learning models. In this paper we explore interpretability of DNN models designed to identify jets coming from top quark decay in high energy proton–proton collisions at the Large Hadron Collider. We review a subset of existing top tagger models and explore different quantitative methods to identify which features play the most important roles in identifying the top jets. We also investigate how and why feature importance varies across different XAI metrics, how correlations among features impact their explainability, and how latent space representations encode information as well as correlate with physically meaningful quantities. Our studies uncover some major pitfalls of existing XAI methods and illustrate how they can be overcome to obtain consistent and meaningful interpretation of these models. We additionally illustrate the activity of hidden layers as neural activation pattern diagrams and demonstrate how they can be used to understand how DNNs relay information across the layers and how this understanding can help to make such models significantly simpler by allowing effective model reoptimization and hyperparameter tuning. These studies not only facilitate a methodological approach to interpreting models but also unveil new insights about what these models learn. Incorporating these observations into augmented model design, we propose the particle flow interaction network model and demonstrate how interpretability-inspired model augmentation can improve top tagging performance.

97 MATHEMATICS AND COMPUTING↗

Machine-learning Kohn–Sham potential from dynamics in time-dependent Kohn–Sham systems

Abstract The construction of a better exchange-correlation potential in time-dependent density functional theory (TDDFT) can improve the accuracy of TDDFT calculations and provide more accurate predictions of the properties of many-electron systems. Here, we propose a machine learning method to develop the energy functional and the Kohn–Sham potential of a time-dependent Kohn–Sham (TDKS) system is proposed. The method is based on the dynamics of the Kohn–Sham system and does not require any data on the exact Kohn–Sham potential for training the model. We demonstrate the results of our method with a 1D harmonic oscillator example and a 1D two-electron example. We show that the machine-learned Kohn–Sham potential matches the exact Kohn–Sham potential in the absence of memory effect. Our method can still capture the dynamics of the Kohn–Sham system in the presence of memory effects. The machine learning method developed in this article provides insight into making better approximations of the energy functional and the Kohn–Sham potential in the TDKS system.

97 MATHEMATICS AND COMPUTING↗

Ergodicity, lack thereof, and the performance of reservoir computing with memristive networks

Abstract Networks composed of nanoscale memristive components, such as nanowire and nanoparticle networks, have recently received considerable attention because of their potential use as neuromorphic devices. In this study, we explore ergodicity in memristive networks, showing that the performance on machine leaning tasks improves when these networks are tuned to operate at the edge between two global stability points. We find this lack of ergodicity is associated with the emergence of memory in the system. We measure the level of ergodicity using the Thirumalai-Mountain metric, and we show that in the absence of ergodicity, two different memristive network systems show improved performance when utilized as reservoir computers (RC). We highlight that it is also important to let the system synchronize to the input signal in order for the performance of the RC to exhibit improvements over the baseline.

97 MATHEMATICS AND COMPUTING↗

A deep learning approach to identify missing is-a relations in SNOMED CT

Abstract Objective SNOMED CT is the largest clinical terminology worldwide. Quality assurance of SNOMED CT is of utmost importance to ensure that it provides accurate domain knowledge to various SNOMED CT-based applications. In this work, we introduce a deep learning-based approach to uncover missing is-a relations in SNOMED CT. Materials and Methods Our focus is to identify missing is-a relations between concept-pairs exhibiting a containment pattern (ie, the set of words of one concept being a proper subset of that of the other concept). We use hierarchically related containment concept-pairs as positive instances and hierarchically unrelated containment concept-pairs as negative instances to train a model predicting whether an is-a relation exists between 2 concepts with containment pattern. The model is a binary classifier leveraging concept name features, hierarchical features, enriched lexical attribute features, and logical definition features. We introduce a cross-validation inspired approach to identify missing is-a relations among all hierarchically unrelated containment concept-pairs. Results We trained and applied our model on the Clinical finding subhierarchy of SNOMED CT (September 2019 US edition). Our model (based on the validation sets) achieved a precision of 0.8164, recall of 0.8397, and F1 score of 0.8279. Applying the model to predict actual missing is-a relations, we obtained a total of 1661 potential candidates. Domain experts performed evaluation on randomly selected 230 samples and verified that 192 (83.48%) are valid. Conclusions The results showed that our deep learning approach is effective in uncovering missing is-a relations between containment concept-pairs in SNOMED CT.

97 MATHEMATICS AND COMPUTING↗

An finite element analysis surrogate model with boundary oriented graph embedding approach for rapid design

Abstract In this work, we present a boundary oriented graph embedding (BOGE) approach for the graph neural network to assist in rapid design and digital prototyping. The cantilever beam problem has been solved as an example to validate its potential of providing physical field results and optimized designs using only 10 ms. Providing shortcuts for both boundary elements and local neighbor elements, the BOGE approach can embed unstructured mesh elements into the graph and performs an efficient regression on large-scale triangular-mesh-based finite element analysis (FEA) results, which cannot be realized by other machine-learning-based surrogate methods. It has the potential to serve as a surrogate model for other boundary value problems. Focusing on the cantilever beam problem, the BOGE approach with 3-layer DeepGCN model achieves the regression with mean square error (MSE) of 0.011 706 (2.41% mean absolute percentage error) for stress field prediction and 0.002 735 MSE (with 1.58% elements having error larger than 0.01) for topological optimization. The overall concept of the BOGE approach paves the way for a general and efficient deep-learning-based FEA simulator that will benefit both industry and Computer Aided Design (CAD) design-related areas.

42 ENGINEERING↗

On the degeneracy of spin ice graphs, and its estimate via the Bethe permanent

The concept of spin ice can be extended to a general graph. We study the degeneracy of spin ice graph on arbitrary interaction structures via graph theory. We map spin ice graphs to the Ising model on a graph and clarify whether the inverse mapping is possible via a modified Krausz construction. From the gauge freedom of frustrated Ising systems, we derive exact, general results about frustration and degeneracy. We demonstrate for the first time that every spin ice graph, with the exception of the one-dimensional Ising model, is degenerate. We then study how degeneracy scales in size, using the mapping between Eulerian trails and spin ice manifolds, and a permanental identity for the number of Eulerian orientations. Furthermore, we show that the Bethe permanent technique provides both an estimate and a lower bound to the frustration of spin ices on arbitrary graphs of even degree. While such a technique can also be used to obtain an upper bound, we find that in all finite degree examples we studied, another upper bound based on Schrijver inequality is tighter.

97 MATHEMATICS AND COMPUTING↗

Dark energy survey year 3 results: Cosmological constraints from cluster abundances, weak lensing, and galaxy clustering

Galaxy clusters provide a unique probe of the late-time cosmic structure and serve as a powerful independent test of the Λ⁢CDM model. This work presents the first set of cosmological constraints derived with ∼16,000 optically selected redMaPPer clusters across nearly 5000 deg 2 using DES year 3 datasets. Our analysis leverages a consistent modeling framework for galaxy cluster cosmology and DES-Y3 joint analyses of galaxy clustering and weak lensing (3 × 2⁢pt), ensuring direct comparability with the DES-Y3 3 × 2⁢pt analysis. Here, we obtain constraints of 𝑆 8 = 0.864 ± 0.035 and Ω m = $0.26⁢5^{+0.019}_{−0.031}$ from the cluster-based data vector. We find that cluster constraints and 3 × 2⁢pt constraints are consistent under the Λ⁢CDM model with a posterior predictive distribution (PPD) value of 0.53. The consistency between clusters and 3 × 2⁢pt provides a stringent test of Λ⁢CDM across different mass and spatial scales. Jointly analyzing clusters with 3 × 2⁢pt further improves cosmological constraints, yielding 𝑆 8 = $0.81⁢1^{+0.022}_{−0.020}$ and Ω m = $0.29⁢4^{+0.022}_{−0.033}$, a 24% improvement in the Ω m − 𝑆 8 figure of merit over 3 × 2⁢pt alone. Moreover, we find no significant deviation from the Planck CMB constraints with a probability to exceed (PTE) value of 0.6, significantly reducing previous 𝑆 8 tension claims. Finally, combining DES 3 × 2⁢pt, DES clusters, and Planck CMB places an upper limit on the sum of neutrino masses of ∑𝑚 𝜈 < 0.26 eV at 95% confidence under the Λ⁢CDM model. These results establish optically selected clusters as a key cosmological probe and pave the way for cluster-based analyses in upcoming stage-IV surveys such as LSST, Euclid, and Roman.

Abbott, T. M. C. [NSF’s National Optical-Infrared ↗

Recovery of Damaged Information and the Out-of-Time-Ordered Correlators

The evolution with a complex Hamiltonian generally leads to information scrambling. A time-reversed dynamics unwinds this scrambling and thus leads to the original information recovery. In this work, we show that if the scrambled information is, in addition, partially damaged by a local measurement, then such a damage can still be treated by application of the time-reversed protocol. This information recovery is described by the long-time saturation value of a certain out-of-time-ordered correlator of local variables. We also propose a simple test that distinguishes between quantum and reversible classical chaotic information scrambling.

97 MATHEMATICS AND COMPUTING↗

Nonadiabatic Phase Transition with Broken Chiral Symmetry

We explore nonadiabatic quantum phase transitions in an Ising spin chain with a linearly time-dependent transverse field and two different spins per unit cell. Such a spin system passes through critical points with gapless excitations, which support nonadiabatic transitions. Nevertheless, we find that the excitations on one of the chain sublattices are suppressed in the nearly adiabatic regime exponentially. Furthermore, we reveal a coherent mechanism to induce exponentially large density separation for different quasiparticles.

1-dimensional spin chains↗

Variational quantum algorithm for estimating the quantum Fisher information

The quantum Fisher information (QFI) quantifies the ultimate precision of estimating a parameter from a quantum state and can be regarded as a reliability measure of a quantum system as a quantum sensor. However, estimation of the QFI for a mixed state is in general a computationally demanding task. In this paper we present a variational quantum algorithm called variational quantum Fisher information estimation (VQFIE) to address this task. By estimating lower and upper bounds on the QFI, based on bounding the fidelity, VQFIE outputs a range in which the actual QFI lies. This result can then be used to variationally prepare the state that maximizes the QFI, for the application of quantum sensing. In contrast to previous approaches, VQFIE does not require knowledge of the explicit form of the sensor dynamics. We simulate the algorithm for a magnetometry setup and demonstrate the tightening of our bounds as the state purity increases. For this example, we compare our bounds with literature bounds and show that our bounds are tighter.

97 MATHEMATICS AND COMPUTING↗