Saibal De

Saibal De, Zitong Li, Hemanth Kolla et al.

The Tucker decomposition, an extension of singular value decomposition for higher-order tensors, is a useful tool in analysis and compression of large-scale scientific data. While it has been studied extensively for static datasets, there are relatively few works addressing the computation of the Tucker factorization of streaming data tensors. In this paper we propose a new streaming Tucker algorithm tailored for scientific data, specifically for the case of a data tensor whose size increases along a single streaming mode that can grow indefinitely, which is typical of time-stepping scientific applications. At any point of this growth, we seek to compute the Tucker decomposition of the data generated thus far, without requiring storing the past tensor slices in memory. Our algorithm accomplishes this by starting with an initial Tucker decomposition and updating its components--the core tensor and factor matrices--with each new tensor slice as it becomes available, while satisfying a user-specified threshold of norm error. We present an implementation within the TuckerMPI software framework, and apply it to synthetic and combustion simulation datasets. By comparing against the standard (batch) decomposition algorithm we show that our streaming algorithm provides significant improvements in memory usage. If the tensor rank stops growing along the streaming mode, the streaming algorithm also incurs less computational time compared to the batch algorithm.

Saibal De, Reese E. Jones, Hemanth Kolla

Stochastic collocation (SC) is a well-known non-intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full-field uncertainty propagation that characterizes the distributions of the high-dimensional primary solution fields of a model with stochastic input parameters. However, due to the highly nonlinear nature of the parameter-to-solution map in even the simplest dynamical systems, the constructed SC surrogates are often inaccurate. This work presents an alternative approach, where we apply the SC approximation over the dynamics of the model, rather than the solution. By combining the data-driven sparse identification of nonlinear dynamics (SINDy) framework with SC, we construct dynamics surrogates and integrate them through time to construct the surrogate solutions. We demonstrate that the SC-over-dynamics framework leads to smaller errors, both in terms of the approximated system trajectories as well as the model state distributions, when compared against full-field SC applied to the solutions directly. We present numerical evidence of this improvement using three test problems: a chaotic ordinary differential equation, and two partial differential equations from solid mechanics.

Saibal De, Oliver Knitter, Rohan Kodati et al.

Variational quantum algorithms (VQAs) are promising hybrid quantum-classical methods designed to leverage the computational advantages of quantum computing while mitigating the limitations of current noisy intermediate-scale quantum (NISQ) hardware. Although VQAs have been demonstrated as proofs of concept, their practical utility in solving real-world problems -- and whether quantum-inspired classical algorithms can match their performance -- remains an open question. We present a novel application of the variational quantum linear solver (VQLS) and its classical neural quantum states-based counterpart, the variational neural linear solver (VNLS), as key components within a minimum map Newton solver for a complementarity-based rigid body contact model. We demonstrate using the VNLS that our solver accurately simulates the dynamics of rigid spherical bodies during collision events. These results suggest that quantum and quantum-inspired linear algebra algorithms can serve as viable alternatives to standard linear algebra solvers for modeling certain physical systems.

James Stokes, Saibal De, Shravan Veerapaneni et al.

We initiate the study of neural-network quantum state algorithms for analyzing continuous-variable lattice quantum systems in first quantization. A simple family of continuous-variable trial wavefunctons is introduced which naturally generalizes the restricted Boltzmann machine (RBM) wavefunction introduced for analyzing quantum spin systems. By virtue of its simplicity, the same variational Monte Carlo training algorithms that have been developed for ground state determination and time evolution of spin systems have natural analogues in the continuum. We offer a proof of principle demonstration in the context of ground state determination of a stoquastic quantum rotor Hamiltonian. Results are compared against those obtained from partial differential equation (PDE) based scalable eigensolvers. This study serves as a benchmark against which future investigation of continuous-variable neural quantum states can be compared, and points to the need to consider deep network architectures and more sophisticated training algorithms.

Saibal De, Hadi Salehi, Alex Gorodetsky

Bayesian low-rank matrix factorization techniques have become an essential tool for relational data analysis and matrix completion. A standard approach is to assign zero-mean Gaussian priors on the columns or rows of factor matrices to create a conjugate system. This choice of prior leads to simple implementations; however it also causes symmetries in the posterior distribution that can severely reduce the efficiency of Markov-chain Monte-Carlo (MCMC) sampling approaches. In this paper, we propose a simple modification to the prior choice that provably breaks these symmetries and maintains/improves accuracy. Specifically, we provide conditions that the Gaussian prior mean and covariance must satisfy so the posterior does not exhibit invariances that yield sampling difficulties. For example, we show that using non-zero linearly independent prior means significantly lowers the autocorrelation of MCMC samples, and can also lead to lower reconstruction errors.