Neural PDE surrogates can improve the cost-accuracy tradeoff of classical solvers, but often generalize poorly to new initial conditions and accumulate errors over time. Physical and symmetry constraints have shown promise in closing this performance gap, but existing techniques for imposing these inductive biases are incompatible with the staggered grids commonly used in computational fluid dynamics. Here we introduce novel input and output layers that respect physical laws and symmetries on the staggered grids, and for the first time systematically investigate how these constraints, individually and in combination, affect the accuracy of PDE surrogates. We focus on two challenging problems: shallow water equations with closed boundaries and decaying incompressible turbulence. Compared to strong baselines, symmetries and physical constraints consistently improve performance across tasks, architectures, autoregressive prediction steps, accuracy measures, and network sizes. Symmetries are more effective than physical constraints, but surrogates with both performed best, even compared to baselines with data augmentation or pushforward training, while themselves benefiting from the pushforward trick. Doubly-constrained surrogates also generalize better to initial conditions and durations beyond the range of the training data, and more accurately predict real-world ocean currents.

For classical PDE solvers, adjusting the spatial resolution and time step offers a trade-off between speed and accuracy. Neural emulators often achieve better speed-accuracy trade-offs by operating on a compact representation of the PDE system. Coarsened PDE fields are a simple and effective representation, but cannot exploit fine spatial scales in the high-fidelity numerical solutions. Alternatively, unstructured latent representations provide efficient autoregressive rollouts, but cannot enforce local interactions or physical laws as inductive biases. To overcome these limitations, we introduce hybrid representations that augment coarsened PDE fields with spatially structured latent variables extracted from high-resolution inputs. Hybrid representations provide efficient rollouts, can be trained on a simple loss defined on coarsened PDE fields, and support hard physical constraints. When predicting fine- and coarse-scale features across multiple PDE emulation tasks, they outperform or match the speed-accuracy trade-offs of the best convolutional, attentional, Fourier operator-based and autoencoding baselines.

Recent advances in probabilistic modelling have led to a large number of simulation-based inference algorithms which do not require numerical evaluation of likelihoods. However, a public benchmark with appropriate performance metrics for such ’likelihood-free’ algorithms has been lacking. This has made it difficult to compare algorithms and identify their strengths and weaknesses. We set out to fill this gap: We provide a benchmark with inference tasks and suitable performance metrics, with an initial selection of algorithms including recent approaches employing neural networks and classical Approximate Bayesian Computation methods. We found that the choice of performance metric is critical, that even state-of-the-art algorithms have substantial room for improvement, and that sequential estimation improves sample efficiency. Neural network-based approaches generally exhibit better performance, but there is no uniformly best algorithm. We provide practical advice and highlight the potential of the benchmark to diagnose problems and improve algorithms. The results can be explored interactively on a companion website. All code is open source, making it possible to contribute further benchmark tasks and inference algorithms.

How can one perform Bayesian inference on stochastic simulators with intractable likelihoods? A recent approach is to learn the posterior from adaptively proposed simulations using neural network-based conditional density estimators. However, existing methods are limited to a narrow range of proposal distributions or require importance weighting that can limit performance in practice. Here we present automatic posterior transformation (APT), a new sequential neural posterior estimation method for simulation-based inference. APT can modify the posterior estimate using arbitrary, dynamically updated proposals, and is compatible with powerful flow-based density estimators. It is more flexible, scalable and efficient than previous simulation-based inference techniques. APT can operate directly on high-dimensional time series and image data, opening up new applications for likelihood-free inference.

Tree-structured computations are relatively easy to process in parallel. As leaf processes are recursively spawned they can be assigned to independent processors in a multicomputer network. However, to achieve good performance the on-line mapping algorithm must maintain load balance, i.e., distribute processes equitably among processors. Additionally, the algorithm itself must be distributed in nature, and process allocation must be completed via message-passing with minimal communication overhead. This paper investigates bounds on the performance of deterministic and randomized algorithms for on-line tree embeddings. In particular, we study trade-offs between computation overhead (load imbalance) and communication overhead (message congestion). We give a simple technique to derive lower bounds on the congestion that any on-line allocation algorithm must incur in order to guarantee load balance. This technique works for both randomized and deterministic algorithms. We prove that the advantage of randomization is limited. Optimal bounds are achieved for several networks, including multidimensional grids and butterflies.

Physical mapping is a fundamental component of the human genome project.A physical map consists of a set of probes which mark unique positions on a long fragment of DNA, together with the relative order of the probes on the DNA.This order is inferred from clone-probe hybridization experiments, which determine the probes contained within various fragments of the genome.In practice, the order of the probes is not completely determined by the hybridization experiments.To better design these experiments, researchers have analyzed the expected distribution of "islands" -groups of probes which are known to be near one another-that would result from hybridization experiments with different numbers of clones and probes.In this paper we analyze the distribution of "runs" -groups of probes whose relative order is completely determined by the hybridization experiment.We include analytic, numerical, Monte Carlo, and simulation results on runs, which can further assist in the design of these experiments.

Large MPP systems can neither solve grand-challenge scientific problems nor enable large scale industrial and governmental simulations if they rely on extensions to workstation system software. At Sandia National Laboratories we have developed, with our vendors, a new system architecture for high-end computing. Highest performance is achieved by providing applications with a light-weight interface to a collection of processing nodes. Usability is provided by creating node partitions specialized for user access, networking, and I/O. The entire system is glued together by a data movement interface which we call portals. Portals allow data to flow between processing nodes with minimal system overhead while maintaining a suitable degree of protection and reconfigurability.

This paper investigates the effects of the failure of shared objects on distributed systems.First the notion of a faulty shared object is introduced.Then upper and lower bounds on the space complexity of implementing reliable shared objects are provided, Shared object failures are modeled as instantaneous and arbitraty changes to the state of the object.Several constructions of nonfaulty wait-free shared objects from a set of shared objects, some of which may suffer any number of faults, are presented.Three of these constructions are: (1) A reliable atomic read/write register from 20~+ 8 atomic read/write registers ~of which may be faulty, (2) a reliable test& set register for n processes from n + 10 primitive test & set registers, one of which may be faulty, and 3n + 13 reliable atomic registers, and (3) a reliable consensus object from 2f + 1 read-modify-write registers when f of these may be faulty.Using these constructions a universal construction of any linearizable shared object from a set of either A preliminary version of the results presented in this paper appeared in

This paper describes three applications of the boundary element method and their implementations on the Intel Paragon supercomputer. Each of these applications sustains over 99 Gflops/s based on wall-clock time for the entire application and an actual count of flops executed; one application sustains over 140 Gflops/s. Each application accepts the description of an arbitrary geometry and computes the solution to a problem of commercial and research interest. The common kernel for these applications is a dense equation solver based on LU factorization. It is generally accepted that good performance can be achieved by dense matrix algorithms, but achieving the excellent performance demonstrated here required the development of a variety of special techniques to take full advantage of the power of the Intel Paragon.>

Chips (or chip sets) which include one or more CPUS, some local memory, and rudimentary communications and routing hardware are becoming common (eg.transputers, SRCS HNet, thenodes ofmost MIMD machines).These chips provide the possibihty of tailoring the topology of a machine to a particular problem.Rather than asking thestandardquestion of how to best coerce one's algorithm to fit an existing topology, one can ask what would be the best topology for the algorithm.This paper defines the efficiency of a topology for an algorithm and gives upper and lower bounds on the best efficiency achievable (as a function of the number of different communication patterns used by the algorithm).This approach is then applied to algorithms which use stencil patterned communications.The result is the definition of topologies which are significantly more efficient than the naive topology.

This paper addresses problems which arise in the synchronization and coordination of distributed systems which employ unreliable shared memory. We present algorithms which solve the consensus problem, and which simulate reliable shared-memory objects, despite the fact that the available memory objects (e.g. read/write registers, test-and-set registers, read-modify-write registers) may be faulty.

Article Free Access Share on Routing multiple paths in hypercubes Authors: D. Greenberg Department of Computer Science, Yale University, New Haven, CT Department of Computer Science, Yale University, New Haven, CTView Profile , S. Bhatt Department of Computer Science, Yale University, New Haven, CT and Computer Science Department, 256-80 California Institute of Technology, Pasadena, CA Department of Computer Science, Yale University, New Haven, CT and Computer Science Department, 256-80 California Institute of Technology, Pasadena, CAView Profile Authors Info & Claims SPAA '90: Proceedings of the second annual ACM symposium on Parallel algorithms and architecturesMay 1990 Pages 45–54https://doi.org/10.1145/97444.97457Published:01 May 1990Publication History 12citation363DownloadsMetricsTotal Citations12Total Downloads363Last 12 Months5Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF