arXiv subjects

Sreeram Venkat

Publications and source records attributed to Sreeram Venkat.

9 recordsLinked to original sources

arXiv2026

Sensor Placement for Tsunami Early Warning via Large-Scale Bayesian Optimal Experimental Design

Real-time tsunami early warning relies on distributed sensor networks to infer seismic sources and seafloor motion. Optimizing these networks via Bayesian optimal experimental design (OED) is exceptionally challenging for systems governed by hyperbolic partial differential equations, which lack the spectral decay required by standard low-rank approximations. We present a scalable Bayesian OED framework for linear time-invariant systems. By reformulating the inverse problem in the data space, we transform OED into dense matrix subset selection. We propose a multi-GPU, Schur-complement-update-based, greedy algorithm that solves the OED problem using a pipelined approach that fully overlaps I/O with GPU computations. Our framework achieves near-perfect weak and strong scaling across hundreds of GPUs on Perlmutter and Frontier. Applied to the 2025 Gordon Bell Prize-winning digital twin for tsunami forecasting in the Cascadia Subduction Zone, we optimize a 175-sensor network, minimizing the uncertainty of a parameter field with over one billion degrees of freedom.

cs.DC↗

arXiv2026

Rapid Earthquake-to-Tsunami Waveform Generation via Large-Scale Multi-GPU FFT Convolution Applied to the Cascadia Subduction Zone

Data-driven methods for earthquake and tsunami early warning rely on large ensembles of rupture scenarios and their resulting waveforms, but generating such datasets with repeated high-fidelity seismic and tsunami simulations is prohibitively expensive. We exploit the linear time-invariant structure of both dynamics to precompute elastic Green's functions and acoustic-gravity adjoint responses, reducing the source-to-waveform map to two consecutive convolution operators. We evaluate these convolutions with a distributed, FFT-accelerated GPU pipeline that partitions the large seafloor grid across GPUs and directly generates the final observation waveforms. We demonstrate the scalability of this pipeline for the Cascadia Subduction Zone with 963 subfaults, 2,416,530 seafloor grid points, 64 observation locations, and 256 timesteps, requiring 9.45 TiB of aggregate GPU memory. On 64 GB200 GPUs within one NVL72 domain, the pipeline generates waveforms in 24 ms per rupture once the response operators are resident, enabling large rupture ensembles to be evaluated within minutes.

cs.DC↗

arXiv2026

Real-time probabilistic tsunami forecasting in Cascadia from sparse offshore pressure observations

Near-field tsunami early warning in the Cascadia Subduction Zone is limited by sparse offshore observations. We investigate whether a hypothetical network of 175 ocean-bottom pressure sensors can support real-time Bayesian inference of the full spatiotemporal seafloor velocity field and probabilistic tsunami forecasting for a margin-wide and a partial fully-coupled Cascadia earthquake dynamic rupture-tsunami scenario. The simulated oceanic acoustic, Rayleigh, and tsunami wavefields are similar during the first two minutes after nucleation but diverge thereafter, enabling rapid earthquake scenario discrimination. Using an acoustic-gravity inversion with assimilation of pressure data, tsunami wave height forecasts are obtained in less than a second. We leverage a Bayesian inversion-based framework that splits the computations into an offline precomputation phase performed with large-scale computing facilities, and an online phase that computes forecasts and can be executed on a laptop. Forecast errors remain low at 22.1% for the margin-wide and 19.6% for the partial rupture.

physics.geo-ph↗

arXiv2026

Goal-Oriented Real-Time Bayesian Inference for Linear Autonomous Dynamical Systems With Application to Digital Twins for Tsunami Early Warning

We present a goal-oriented framework for constructing digital twins with the following properties: (1) they employ discretizations of high-fidelity PDE models governed by autonomous dynamical systems, leading to large-scale forward problems; (2) they solve a linear inverse problem to assimilate observational data to infer uncertain model components followed by a forward prediction of the evolving dynamics; and (3) the entire end-to-end, data-to-inference-to-prediction computation is carried out without approximation and in real time through a Bayesian framework that rigorously accounts for uncertainties. Several challenges must be overcome to realize this framework, including the large scale of the forward problem, the high dimensionality of the parameter space, and for a class of problems including those we target, the slow decay of the singular values of the parameter-to-observable map. Here we introduce a methodology to overcome these challenges by exploiting the autonomous structure of the forward model to decompose the solution of the inverse problem into an offline phase in which the PDE model is solved a limited number of times, and an online phase that computes the parameter inference and prediction of quantities of interest in real time, given observational data. Our goal is to apply this framework to construct digital twins for subduction zones to provide early warning for tsunamis. To this end, we show how our methodology can be used to employ seafloor pressure observations, along with the coupled acoustic-gravity wave equations, to infer the earthquake-induced seafloor motion (discretized with 10^9 parameters) and forecast the tsunami propagation. We present results of an end-to-end inference, prediction, and uncertainty quantification for a representative test problem with 10^8 inversion parameters for which goal-oriented Bayesian inference is accomplished in real time.

math.NA↗

arXiv2025

Mixed-Precision Performance Portability of FFT-Based GPU-Accelerated Algorithms for Block-Triangular Toeplitz Matrices

The hardware diversity in leadership-class computing facilities, alongside the immense performance boosts from today's GPUs when computing in lower precision, incentivizes scientific HPC workflows to adopt mixed-precision algorithms and performance portability models. We present an on-the-fly framework using hipify for performance portability and apply it to FFTMatvec - an HPC application that computes matrix-vector products with block-triangular Toeplitz matrices. Our approach enables FFTMatvec, initially a CUDA-only application, to run seamlessly on AMD GPUs with excellent performance. Performance optimizations for AMD GPUs are integrated into the open-source rocBLAS library, keeping the application code unchanged. We then present a dynamic mixed-precision framework for FFTMatvec; a Pareto front analysis determines the optimal mixed-precision configuration for a desired error tolerance. Results are shown for AMD Instinct MI250X, MI300X, and the newly launched MI355X GPUs. The performance-portable, mixed-precision FFTMatvec is scaled to 4,096 GPUs on the OLCF Frontier supercomputer.

cs.DC↗

arXiv2025

Real-time Bayesian inference at extreme scale: A digital twin for tsunami early warning applied to the Cascadia subduction zone

We present a Bayesian inversion-based digital twin that employs acoustic pressure data from seafloor sensors, along with 3D coupled acoustic-gravity wave equations, to infer earthquake-induced spatiotemporal seafloor motion in real time and forecast tsunami propagation toward coastlines for early warning with quantified uncertainties. Our target is the Cascadia subduction zone, with one billion parameters. Computing the posterior mean alone would require 50 years on a 512 GPU machine. Instead, exploiting the shift invariance of the parameter-to-observable map and devising novel parallel algorithms, we induce a fast offline-online decomposition. The offline component requires just one adjoint wave propagation per sensor; using MFEM, we scale this part of the computation to the full El Capitan system (43,520 GPUs) with 92% weak parallel efficiency. Moreover, given real-time data, the online component exactly solves the Bayesian inverse and forecasting problems in 0.2 seconds on a modest GPU system, a ten-billion-fold speedup.

cs.DC↗

arXiv2025

Fast And Scalable FFT-Based GPU-Accelerated Algorithms for Block-Triangular Toeplitz Matrices With Application to Linear Inverse Problems Governed by Autonomous Dynamical Systems

We present an efficient and scalable algorithm for performing matrix-vector multiplications ("matvecs") for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving inverse problems governed by autonomous systems, and time-invariant systems in particular. In this article, we consider inverse problems that infer unknown parameters from observational data of a linear time-invariant dynamical system given in the form of partial differential equations (PDEs). Matrix-free Newton-conjugate-gradient methods are often the gold standard for solving these inverse problems, but they require numerous actions of the Hessian on a vector. Matrix-free adjoint-based Hessian matvecs require solution of a pair of linearized forward/adjoint PDE solves per Hessian action, which may be prohibitive for large-scale inverse problems. Time invariance of the forward PDE problem leads to a block Toeplitz structure of the discretized parameter-to-observable (p2o) map defining the mapping from inputs (parameters) to outputs (observables) of the PDEs. This block Toeplitz structure enables us to exploit two key properties: (1) compact storage of the p2o map and its adjoint; and (2) efficient fast Fourier transform (FFT)-based Hessian matvecs. The proposed algorithm is mapped onto large multi-GPU clusters and achieves more than 80 percent of peak bandwidth on NVIDIA A100 GPUs. Excellent weak scaling is shown for up to 48 A100 GPUs. For the targeted problems, the implementation executes Hessian matvecs within fractions of a second, which is orders of magnitude faster than can be achieved by conventional matrix-free Hessian matvecs via forward/adjoint PDE solves.

math.NA↗

arXiv2021

Convolutional Autoencoders for Reduced-Order Modeling

In the construction of reduced-order models for dynamical systems, linear projection methods, such as proper orthogonal decompositions, are commonly employed. However, for many dynamical systems, the lower dimensional representation of the state space can most accurately be described by a \textit{nonlinear} manifold. Previous research has shown that deep learning can provide an efficient method for performing nonlinear dimension reduction, though they are dependent on the availability of training data and are often problem-specific \citep[see][]{carlberg_ca}. Here, we utilize randomized training data to create and train convolutional autoencoders that perform nonlinear dimension reduction for the wave and Kuramoto-Shivasinsky equations. Moreover, we present training methods that are independent of full-order model samples and use the manifold least-squares Petrov-Galerkin projection method to define a reduced-order model for the heat, wave, and Kuramoto-Shivasinsky equations using the same autoencoder.

math.DS↗

arXiv2021

Sobolev Orthogonal Polynomials on the Sierpinski Gasket

We develop a theory of Sobolev orthogonal polynomials on the Sierpiński gasket ($SG$). These orthogonal polynomials arise through the Gram-Schmidt orthogonalisation process applied on the set of monomials on $SG$ using several notions of a Sobolev inner products. After establishing some recurrence relations for these orthogonal polynomials, we give estimates for their $L^2$, $L^\infty$ and Sobolev norms, and study their asymptotic behaviour. Finally, we study the properties of zero sets of polynomials and develop fast computational tools to explore applications to quadrature and interpolation.

math.CA↗