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Twisted Supergravity and Koszul Duality: A Case Study in AdS 3
In this note, we study a simplified variant of the familiar holographic duality between supergravity on AdS 3 × S 3 × T 4 and the SCFT (on the moduli space of) the symmetric orbifold theory Sym N (T 4 ) as N → ∞. This variant arises conjecturally from a twist proposed by the first author and Si Li. We recover a number of results concerning protected subsectors of the original duality working directly in the twisted bulk theory. Moreover, we identify the symmetry algebra arising in the N → ∞ limit of the twisted gravitational theory. Further, we emphasize the role of Koszul duality—a ubiquitous mathematical notion to which we provide a friendly introduction—in field theory and string theory. After illustrating the appearance of Koszul duality in the “toy” example of holomorphic Chern-Simons theory, we describe how (a deformation of) Koszul duality relates bulk and boundary operators in our twisted setup, and explain how one can compute algebra OPEs diagrammatically using this notion. Further details, results, and computations will appear in a companion paper.
Spatiotemporal pattern detection, generation, and computation with circuits
Abstract Implementations of neurons, delays, and synapse circuits are presented with simulations. These neural elements are used to create two small spiking neural networks, the Rate-Window and Order-Biased clusters, which are capable of detecting simple two-spike spatiotemporal patterns. A simple pattern detecting network (SPDN) is created by combining the Rate-Window and Order-Biased clusters, where clusters are small spiking neural networks, and its simple pattern detection ability is demonstrated in simulation. The SPDN is used to implement a complex pattern detecting network (CPDN) and its complex pattern detection ability is demonstrated in simulation. Methods for generating arbitrary spatiotemporal patterns are presented. The CPDN and spatiotemporal pattern generation methods are then used to implement a novel spatiotemporal computing paradigm based on detecting and responding to spatiotemporal symbols. A simulation of a spatiotemporal half adder is presented to demonstrate the computing paradigm.
An Efficient Numerical Algorithm for Solving Data Driven Feedback Control Problems
The goal of this paper is to solve a class of stochastic optimal control problems numerically, in which the state process is governed by an Itô type stochastic differential equation with control process entering both in the drift and the diffusion, and is observed partially. The optimal control of feedback form is determined based on the available observational data. In this work, we call this type of control problems the data driven feedback control. The computational framework that we introduce to solve such type of problems aims to find the best estimate for the optimal control as a conditional expectation given the observational information. To make our method feasible in providing timely feedback to the controlled system from data, we develop an efficient stochastic optimization algorithm to implement our computational framework.
Distributed intelligence and the equivalence of matter and information
Here, it is argued that science of discontinua represents a major paradigm shift in how scientific research is done. First, a historical perspective is given, followed by key aspects of discontinuum simulations and its potential in aiding research and development. This is followed by a philosophical perspective on equivalence of matter and information as inspired by Aristotle’s quest for souls in living things such as cells. Finally, the universality of the discontinuum approach is explored with its consequences for computing and artificial intelligence.
Machine-learning-based spectral methods for partial differential equations
Spectral methods are an important part of scientific computing’s arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the solution of a PDE. The last decade has seen the emergence of deep learning as a strong contender in providing efficient representations of complex functions. In the current work, we present an approach for combining deep neural networks with spectral methods to solve PDEs. In particular, we use a deep learning technique known as the Deep Operator Network (DeepONet) to identify candidate functions on which to expand the solution of PDEs. We have devised an approach that uses the candidate functions provided by the DeepONet as a starting point to construct a set of functions that have the following properties: (1) they constitute a basis, (2) they are orthonormal, and (3) they are hierarchical, i.e., akin to Fourier series or orthogonal polynomials. We have exploited the favorable properties of our custom-made basis functions to both study their approximation capability and use them to expand the solution of linear and nonlinear time-dependent PDEs. The proposed approach advances the state of the art and versatility of spectral methods and, more generally, promotes the synergy between traditional scientific computing and machine learning.
A feasible approach for automatically differentiable unitary coupled-cluster on quantum computers
We develop computationally affordable and encoding independent gradient evaluation procedures for unitary coupled-cluster type operators, applicable on quantum computers.
Active readout-error mitigation
Mitigating errors is a significant challenge for near-term quantum computers. One of the most important sources of errors is related to the readout of the quantum state into a classical bit stream. A variety of techniques have been proposed to mitigate these errors with post-hoc corrections. Here, we propose a complementary scheme to actively reduce readout errors on a shot-by-shot basis by encoding single qubits, immediately prior to readout, into multiqubit states. The computational resources of our technique are independent of the circuit depth and are compatible with the error rates and connectivity of many current devices. We analyze the potential of our approach using two types of error-correcting codes, and, as a proof of principle, we demonstrate an 80% improvement in readout error on the IBMQ Mumbai quantum computer.
A Semi-Analytical Solution Approach for Solving Constant-Coefficient First-Order Partial Differential Equations
Simulation and control of many dynamic systems involve solving partial differential equations (PDE). This letter proposes a semi-analytical solution (SAS) approach for fast and high-quality solution of first-order PDEs. The region of interest of the studied PDE is divided into a grid, and an SAS is derived for each grid cell in the form of the multivariate polynomials, of which the coefficients are identified using initial value and boundary value conditions. The solutions are solved in a “time-stepping” manner, i.e. within one time step, the coefficients of the SAS are identified and the initial value of the next time step is evaluated. This approach achieves a significantly larger grid cell than the widely used finite difference method, and thus enhances the computational efficiency significantly. Furthermore, the simulation result on the natural gas pipeline model demonstrates the advantages of SAS in accuracy and computational efficiency.
Trigger-based Incremental Data Processing with Unified Sync and Async Model
In recent years, more and more applications in the cloud have needs to process large-scale on-line datasets, which evolve over time as new entries are added and existing entries are modified. Several programming frameworks, such as Percolator and Oolong, are proposed for such incremental data processing and can achieve efficient processing with an event-driven abstraction. However, these frameworks are inherently asynchronous, leaving the heavy burden of managing synchronization to applications' developers, which further significantly restricts their usabilities. In this study, we propose a trigger-based incremental computing framework in the cloud, called Domino, with both synchronous and asynchronous mechanisms to coordinate parallel triggers. With this new framework, both synchronous and asynchronous applications can be seamlessly developed. Use cases and extensive evaluation results confirm that it can deliver sufficient performance, and also is easy to use for incremental applications in large-scale distributed computing.
Synchronous and Concurrent Multidomain Computing Method for Cloud Computing Platforms
We present a numerical method for synchronous and concurrent solution of transient elastodynamics problem where the computational domain is divided into subdomains that may reside on separate computational platforms. Here, this work employs the variational multiscale discontinuous Galerkin (VMDG) method to develop interdomain transmission conditions for transient problems. The fine-scale modeling concept leads to variationally consistent coupling terms at the common interfaces. The method admits a large class of time discretization schemes, and decoupling of the solution for each subdomain is achieved by selecting any explicit algorithm. Numerical tests with a manufactured solution problem show optimal convergence rates. The energy history in a free vibration problem is in agreement with that of the solution from a monolithic computational domain.
Enumeration reduction algorithm for the characterization of multi-primary LED systems
Multi-primary tunable LED lighting systems can generate a vast number of spectral outputs, with the exact number depending on the resolution of the control signal and number of LED primaries. Computing all combinations to identify optimal spectral power distributions (SPDs) with a specified chromaticity would require a tremendous amount of time and computational power. Here, an enumeration reduction (ER) algorithm is described to reduce the computation time by defining a bounding pyramid in the three-dimensional tristimulus space that maps to the circumscribed square of the target region in the chromaticity diagram. This method enables computing only the necessary amount of tristimulus values (and resulting chromaticity coordinates) for SPDs that fall into a user-defined target chromaticity area, reducing computation time by avoiding the need to generate each combination and calculate its chromaticity coordinates. The results show that the proposed ER algorithm can greatly reduce the time – up to 922 times in a series of tests – to determine a set of metamers compared to a full enumeration computation.
Development and Validation of a Simulation Tool to Predict the Combined Structural, Electrical, Electrochemical and Thermal Responses of Automotive Batteries
Battery safety is one of the most important design factors of electrified vehicles (EVs) since battery failure may lead to a catastrophic consequence. To improve the safety of battery systems in EVs, battery behaviors under various abuse conditions should be well understood. One way to examine battery response under extreme conditions is to conduct abuse tests in different scenarios. They can provide first-hand pass/fail information on battery safety, but they are usually expensive and time-consuming, which is inconvenient during design iterations and optimization. On the other hand, computational modeling can predict the battery behaviors in a more efficient and cost-effective way, which becomes an important tool to evaluate battery safety. Modeling battery responses and failure is challenging since it involves multiple coupled physical processes, needs to consider complex material properties and is computationally intensive. This project aims to develop a practical simulation tool to predict the combined structural, electrical, electrochemical, and thermal responses of automotive batteries to crash-induced crush and short circuit and validate it for conditions relevant to automotive crash. Advanced material constitutive models will be utilized to capture the mechanical response of cell components. Moreover, methods will be developed to reduce computational complexity of the model and allow battery safety simulations to extend from cell-level to module/pack level with affordable computational resources.
Parallelization and Performance Portability in Hydrodynamics Codes
With the eve of Exascale computing, performance and portability are at the forefront of all scientific codes. Adding more cores and more energy to a system is no longer a sustainable way to achieve performance, and extra effort must now be made to improve performance in all areas of code and code development. Using hydrodynamic codes as a basis, this work explores numerous techniques to achieve performance in different ways. Adaptive mesh refinement (AMR) is a necessary technique to improve memory optimization in mesh-based simulations. However it is invasive and conventionally difficult to integrate into existing applications, so we present a new branch of AMR to create a smooth transition to these optimizations, which not only improves performance, but also greatly reduces developer effort. We introduce the concept of this improvement as Phantom-Cell AMR, and assess theoretically the improvements, as well as present an application of its use. Other work included involves and investigation into an efficient data structure that ensures optimal memory layout for cache performance, with a target of making codes performant and portable across all architectures. All of the work targets both performance and portability, not just on CPU hardware, but specifically across GPU architectures. Parallel performance is key to all of the methods presented, but the research makes a great effort to improve the portability of all applications to prepare for current high performance computing systems and those on the horizon.
ECP Milestone Memo WBS 2.3.4.13 ECP/VTK-m FY20Q4 STDA05-54
A memo concerning the status of the Exascale Computing Project (ECP) STDA05-54 is given.
An MLE Approach to Metrology of Laser Propagation Axes using a-Posteriori Uncertainty Estimates Determined Through Monte-Carlo Experimentation
Presentation for minisymposium: Applied Physics Research within the Department of Energy, March 1, 2021. SIAM Conference for Computational Science & Engineering 2021
Codesign for the Masses
In this position paper we will address challenges and opportunities relating to the design and codesign of application specific circuits. Given our background as computational scientists, our perspective is from the viewpoint of a highly motivated application developer as opposed to career computer architects
Understanding Discrete Fracture Networks Through Spectral Graph Theory [Slides]
This presentation includes discussion of the use of spectral graph theory to understand fracture networks to reduce computational effort.