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Outline: Describe principle of magnetically-confined nuclear fusion; Explain the role of Poincaré maps in fusion reactor design; Describe a new method for rapidly computing Poincaré maps using physics-informed machine learning
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Probabilistic computing is a paradigm in which data are not represented by stable bits, but rather by the probability of a metastable bit to be in a particular state. The development of this technology has been hindered by the availability of hardware capable of generating stochastic and tunable sequences of “1s” and “0s”. The options are currently limited to complex CMOS circuitry and, recently, magnetic tunnel junctions. Here, we demonstrate that metal–insulator transitions can also be used for this purpose. We use an electrical pump/probe protocol and take advantage of the stochastic relaxation dynamics in VO 2 to induce random metallization events. A simple latch circuit converts the metallization sequence into a random stream of 1s and 0s. The resetting pulse in between probes decorrelates successive events, providing a true stochastic digital sequence.
We present a method to approximate partition functions of quantum systems using mixed-state quantum computation. For positive-semidefinite Hamiltonians, our method has an expected running-time that is almost linear in [M/( ε rel Z )] 2 , where M is the dimension of the quantum system, Z is the partition function, and ε rel is the relative precision. It is based on approximations of the exponential operator as linear combinations of certain operators related to block-encoding of Hamiltonians or Hamiltonian evolutions. The trace of each operator is estimated using a standard algorithm in the one-clean-qubit model. For large values of Z , our method may run faster than exact classical methods, whose complexities are polynomial in M . We also prove that a version of the partition function estimation problem within additive error is complete for the so-called DQC1 complexity class, suggesting that our method provides a superpolynomial speedup for certain parameter values. Overall, to attain a desired relative precision, we develop a classical procedure based on a sequence of approximations within predetermined additive errors that may be of independent interest.
In the present study, a consistent and conservative Phase-Field method, including both the model and scheme, is developed for multiphase flows with an arbitrary number of immiscible and incompressible fluid phases. The consistency of mass conservation and the consistency of mass and momentum transport are implemented to address the issue of physically coupling the Phase-Field equation, which locates different phases, to the hydrodynamics. These two consistency conditions, as illustrated, provide the “optimal” coupling because (i) the new momentum equation resulting from them is Galilean invariant and implies the kinetic energy conservation, regardless of the details of the Phase-Field equation, and (ii) failures of satisfying the second law of thermodynamics or the consistency of reduction of the multiphase flow model only result from the same failures of the Phase-Field equation but are not due to the new momentum equation. Physical interpretation of the consistency conditions and their formulations are first provided, and general formulations that are obtained from the consistency conditions and independent of the interpretation of the velocity are summarized. Then, the present consistent and conservative multiphase flow model is completed by selecting a reduction consistent Phase-Field equation. Several novel techniques are developed to inherit the physical properties of the multiphase flows after discretization, including the gradient-based phase selection procedure, the momentum conservative method for the surface force, and the general theorems to preserve the consistency conditions on the discrete level. Equipped with those novel techniques, a consistent and conservative scheme for the present multiphase flow model is developed and analyzed. The scheme satisfies the consistency conditions, conserves the mass and momentum, and assures the summation of the volume fractions to be unity, on the fully discrete level and for an arbitrary number of phases. All those properties are numerically validated. Finally, numerical applications demonstrate that the present model and scheme are robust and effective in studying complicated multiphase dynamics, especially for those with large-density ratios.
Popular computational catalyst design strategies rely on the identification of reactivity descriptors, which can be used along with Brønsted–Evans–Polanyi (BEP) and scaling relations as input to a microkinetic model (MKM) to make predictions for activity or selectivity trends. The main benefit of this approach is related to the inherent dimensionality reduction of the large material space to just a few catalyst descriptors. Conversely, it is well documented that a small set of descriptors is insufficient to capture the intricacies and complexities of a real catalytic system. The inclusion of coverage effects through lateral adsorbate-adsorbate interactions can narrow the gap between simplified descriptor predictions and real systems, but mean-field MKMs cannot properly account for local coverage effects. This shortcoming of the mean-field approximation can be rectified by switching to a lattice-based kinetic Monte Carlo (kMC) method using cluster expansion representation of adsorbate–adsorbate lateral interactions. Using the prototypical CO oxidation reaction as an example, we critically evaluate the benefits of kMC over MKM in terms of trend predictions and computational cost when using only a small set of input parameters. After confirming that in the absence of lateral interactions the kMC and MKM approaches yield identical trends and mechanistic information, we observed substantial differences between the two kinetic models when lateral interactions were introduced. Here, the mean-field implementation applies coverage corrections directly to the descriptors, causing an artificial overprediction of the activity of strongly binding metals. In contrast, the cluster expansion in kMC implementation can differentiate among the highly active metals but it is very sensitive to the set of included interaction parameters. Considering that computational screening relies on a minimal set of descriptors, for which MKM makes reasonable trend predictions at a ca. three orders of magnitude lower computational cost than kMC, the MKM approach does provide a better entry point for computational catalyst design.
We propose a scalable framework for the learning of high-dimensional parametric maps via adaptively constructed residual network (ResNet) maps between reduced bases of the inputs and outputs. When just few training data are available, it is beneficial to have a compact parametrization in order to ameliorate the ill-posedness of the neural network training problem. By linearly restricting high-dimensional maps to informed reduced bases of the inputs, one can compress high-dimensional maps in a constructive way that can be used to detect appropriate basis ranks, equipped with rigorous error estimates. A scalable neural network learning framework is thus to learn the nonlinear compressed reduced basis mapping. Unlike the reduced basis construction, however, neural network constructions are not guaranteed to reduce errors by adding representation power, making it difficult to achieve good practical performance. Inspired by recent approximation theory that connects ResNets to sequential minimizing flows, we present an adaptive ResNet construction algorithm. This algorithm allows for depth-wise enrichment of the neural network approximation, in a manner that can achieve good practical performance by first training a shallow network and then adapting. We prove universal approximation of the associated neural network class for $L^2_v$ functions on compact sets. Our overall framework allows for constructive means to detect appropriate breadth and depth, and related compact parametrizations of neural networks, significantly reducing the need for architectural hyperparameter tuning. Numerical experiments for parametric PDE problems and a 3D CFD wing design optimization parametric map demonstrate that the proposed methodology can achieve remarkably high accuracy for limited training data, and outperformed other neural network strategies we compared against.
Software simulators play a critical role in the development of new algorithms and system architectures in any field of engineering. Neuromorphic computing, which has shown potential in building brain-inspired energy-efficient hardware, suffers a slow-down in the development cycle due to a lack of flexible and easy-to-use simulators of either neuromorphic hardware itself or of spiking neural networks (SNNs), the type of neural network computation executed on most neuromorphic systems. While there are several openly available neuromorphic or SNN simulation packages developed by a variety of research groups, they have mostly targeted computational neuroscience simulations, and only a few have targeted small-scale machine learning tasks with SNNs. Evaluations or comparisons of these simulators have often targeted computational neuroscience-style workloads. In this work, we seek to evaluate the performance of several publicly available SNN simulators with respect to non-computational neuroscience workloads, in terms of speed, flexibility, and scalability. We evaluate the performance of the NEST, Brian2, Brian2GeNN, BindsNET and Nengo packages under a common front-end neuromorphic framework. Our evaluation tasks include a variety of different network architectures and workload types to mimic the computation common in different algorithms, including feed-forward network inference, genetic algorithms, and reservoir computing. We also study the scalability of each of these simulators when running on different computing hardware, from single core CPU workstations to multi-node supercomputers. Our results show that the BindsNET simulator has the best speed and scalability for most of the SNN workloads (sparse, dense, and layered SNN architectures) on a single core CPU. However, when comparing the simulators leveraging the GPU capabilities, Brian2GeNN outperforms the others for these workloads in terms of scalability. NEST performs the best for small sparse networks and is also the most flexible simulator in terms of reconfiguration capability NEST shows a speedup of at least 2x compared to the other packages when running evolutionary algorithms for SNNs. The multi-node and multi-thread capabilities of NEST show at least 2x speedup compared to the rest of the simulators (single core CPU or GPU based simulators) for large and sparse networks. We conclude our work by providing a set of recommendations on the suitability of employing these simulators for different tasks and scales of operations. We also present the characteristics for a future generic ideal SNN simulator for different neuromorphic computing workloads.
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Quantum chemistry is regarded to be one of the first disciplines that will be revolutionized by quantum computing. Although universal quantum computers of practical scale may be years away, various approaches are currently being pursued to solve quantum chemistry problems on near-term gate-based quantum computers and quantum annealers by developing the appropriate algorithm and software base. This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. The approach is based on the matrix formulation, efficiently uses qubit resources based on a power-of-two encoding scheme and is hardware-dominant relying on only one classically optimized parameter. We demonstrate the use of D-Wave hardware for obtaining ground and excited electronic states across a variety of small molecular systems. The approach can be adapted for use by a vast majority of electronic structure methods currently implemented in conventional quantum-chemical packages. The results of this work will encourage further development of software such as qbsolv which has promising applications in emerging quantum information processing hardware and has expectation to address large and complex optimization problems intractable for classical computers.
Abstract Only a subset of degrees of freedom are typically accessible or measurable in real-world systems. As a consequence, the proper setting for empirical modeling is that of partially-observed systems. Notably, data-driven models consistently outperform physics-based models for systems with few observable degrees of freedom; e.g. hydrological systems. Here, we provide an operator-theoretic explanation for this empirical success. To predict a partially-observed system’s future behavior with physics-based models, the missing degrees of freedom must be explicitly accounted for using data assimilation and model parametrization. Data-driven models, in contrast, employ delay-coordinate embeddings and their evolution under the Koopman operator to implicitly model the effects of the missing degrees of freedom. We describe in detail the statistical physics of partial observations underlying data-driven models using novel maximum entropy and maximum caliber measures. The resulting nonequilibrium Wiener projections applied to the Mori–Zwanzig formalism reveal how data-driven models may converge to the true dynamics of the observable degrees of freedom. Additionally, this framework shows how data-driven models infer the effects of unobserved degrees of freedom implicitly, in much the same way that physics models infer the effects explicitly. This provides a unified implicit-explicit modeling framework for predicting partially-observed systems, with hybrid physics-informed machine learning methods combining both implicit and explicit aspects.
Readout errors on near-term quantum computers can introduce significant error to the empirical probability distribution sampled from the output of a quantum circuit. These errors can be mitigated by classical postprocessing given the access of an experimental response matrix that describes the error associated with the measurement of each computational basis state. However, the resources required to characterize a complete response matrix and to compute the corrected probability distribution scale exponentially with the number of qubits, n . In this work, we modify standard matrix inversion techniques using perturbative approximations with significantly reduced complexity and bounded error when the likelihood of high-order bit-flip events is strongly suppressed. Given a characteristic error rate q , we discuss a method to recover the probability of the all-zeros bit string p 0 by sampling only a small subspace of the response matrix before inverting readout error, resulting in a relative speedup of poly [ 2 n / ( n w ) ] , which we motivate using a simplified error model for which the approximation incurs only O ( q w ) error for some integer w . We then provide a generalized technique to efficiently recover full output distributions with O ( q w ) error in the perturbative limit. These approximate techniques for readout-error correction may greatly accelerate near-term quantum computing applications.
Here, we numerically examine a bidisperse system of active and passive particles coupled to a resource substrate. The active particles deplete the resource at a fixed rate and move toward regions with higher resources, while all of the particles interact sterically with each other. We show that at high densities, this system exhibits a rich variety of pattern-forming phases along with directed motion or flocking as a function of the relative rates of resource absorption and consumption as well as the active to passive particle ratio. These include partial phase separation into rivers of active particles flowing through passive clusters, strongly phase separated states where the active particles induce crystallization of the passive particles, mixed jammed states, and fluctuating mixed fluid phases. For higher resource recovery rates, we demonstrate that the active particles can undergo motility-induced phase separation, while at high densities, there can be a coherent flock containing only active particles or a solid mixture of active and passive particles. The directed flocking motion typically shows a transient in which the flow switches among different directions before settling into one direction, and there is a critical density below which flocking does not occur. We map out the different phases as function of system density, resource absorption and recovery rates, and the ratio of active to passive particles.
Scientific applications often require high-bandwidth shared storage to perform joint simulations and collaborative data analytics. Shared memory pools provide a chance to satisfy such needs. Recently, a high-speed network such as Gen-Z utilizing persistent memory (PM) offers an opportunity to create a shared memory pool connected to compute nodes. However, there are several challenges to use scientific applications on the shared memory pool directly such as scalability, failure-atomicity, and lack of scientific metadata-based search and query. In this paper, we propose MOSIQS, a persistent memory object storage framework with metadata indexing and querying for scientific computing. We design MOSIQS based on the key idea that memory objects on PM pool can live beyond the application lifetime and can become the sharing currency for applications and scientists. MOSIQS provides an aggregate memory pool atop an array of persistent memory devices to store and access memory objects to accelerate scientific computing. MOSIQS uses a lightweight persistent memory key-value store to manage the metadata of memory objects, which enables memory object sharing. To facilitate metadata search and query over millions of memory objects resident on memory pool, we introduce Group Split and Merge (GSM), a novel persistent index data structure designed primarily for scientific datasets. GSM splits and merges dynamically to minimize the query search space and maintains low query processing time while overcoming the index storage overhead. MOSIQS is implemented on top of PMDK. We evaluate the proposed approach on many-core server with an array of real PM devices. Experimental results show that MOSIQS gains a 100% write performance improvement and executes multi-attribute queries efficiently with 2.7× less index storage overhead offering significant potential to speed up scientific computing applications.
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Abstract-Quantum computing promises potential for science and industry by solving certain computationally complex problems faster than classical computers. Quantum computing systems evolved from coupled to classical computing nodes (HPC). With the increasing monolithic systems towards modular architectures comprising multiple quantum processing units (QPUs) scale, middleware systems that facilitate the efficient coupling of quantum-classical computing are becoming critical. Through an in-depth analysis of quantum applications, integration patterns and systems, we identified a gap in understanding Quantum HPC middleware systems. We present a conceptual middleware to facilitate reasoning about quantum-classical integration and serve as the basis for a future middleware system. An essential contribution of this paper lies in leveraging well-established high performance computing abstractions for managing workloads, tasks, and resources to integrate quantum computing into HPC systems seamlessly