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The numerical integration of stochastic trajectories to estimate the time to pass a threshold is an interesting physical quantity, for instance in Josephson junctions and atomic force microscopy, where the full trajectory is not accessible.…
Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this…
We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…
We present new algorithms for computing and approximating bisimulation metrics in Markov Decision Processes (MDPs). Bisimulation metrics are an elegant formalism that capture behavioral equivalence between states and provide strong…
Parallel algorithms on CPU and GPU are implemented for the Unified Gas-Kinetic Scheme and their performances are investigated and compared by a two dimensional channel flow case. The parallel CPU algorithm has a one dimensional block…
One key challenge for solving a general stochastic optimization problem with expectations in the objective and constraint functions using ordinary stochastic iterative methods lies in the infeasibility issue caused by the randomness over…
Markov chain Monte Carlo is an inherently serial algorithm. Although likelihood calculations for individual steps can sometimes be parallelized, the serial evolution of the process is widely viewed as incompatible with parallelization,…
This article deals with stochastic processes endowed with the Markov (memoryless) property and evolving over general (uncountable) state spaces. The models further depend on a non-deterministic quantity in the form of a control input, which…
Recently, a new variant of the BiCGStab method, known as the pipeline BiCGStab, has been proposed. This method can achieve a higher degree of scalability and speed-up rates through a mechanism in which the communication phase for the…
We present new versions of the previously published C and CUDA programs for solving the dipolar Gross-Pitaevskii equation in one, two, and three spatial dimensions, which calculate stationary and non-stationary solutions by propagation in…
We present a variant of the s-step Preconditioned Conjugate Gradient (PCG) method that combines a Chebyshev-stabilized Krylov basis with a Forward Gauss-Seidel (FGS) iteration for the solution of the reduced Gram systems. In s-step…
The pricing of American style and multiple exercise options is a very challenging problem in mathematical finance. One usually employs a Least-Square Monte Carlo approach (Longstaff-Schwartz method) for the evaluation of conditional…
The linear conjugate gradient method is widely used in physical simulation, particularly for solving large-scale linear systems derived from Newton's method. The nonlinear conjugate gradient method generalizes the conjugate gradient method…
This paper studies parametric Markov decision processes (pMDPs), an extension to Markov decision processes (MDPs) where transitions probabilities are described by polynomials over a finite set of parameters. Fixing values for all parameters…
In this paper, we present, evaluate and analyse the performance of parallel synchronous Jacobi algorithms by different partitioned procedures including band-row splitting, band-row sparsity pattern splitting and substructuring splitting,…
We consider concurrent games played on graphs. At every round of a game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety…
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…
Basic Parallel Processes (BPPs) are a well-known subclass of Petri Nets. They are the simplest common model of concurrent programs that allows unbounded spawning of processes. In the probabilistic version of BPPs, every process generates…
Markov Chain Monte Carlo (MCMC) methods such as Gibbs sampling are finding widespread use in applied statistics and machine learning. These often lead to difficult computational problems, which are increasingly being solved on parallel and…
Scalable Gaussian process (GP) inference is essential for sequential decision-making tasks, yet improving GP scalability remains a challenging problem with many open avenues of research. This paper focuses on iterative GPs, where iterative…