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This draft suggests a new counterexample guided abstraction refinement (CEGAR) framework that uses the combination of numerical simulation for nonlinear differential equations with linear programming for linear hybrid automata (LHA) to…
In this work, we make two improvements on the staggered grid hydrodynamics (SGH) Lagrangian scheme for modeling 2-dimensional compressible multi-material flows on triangular mesh. The first improvement is the construction of a dynamic local…
We develop a multiscale hybrid scheme for simulations of soft condensed matter systems, which allows one to treat the system at the particle level in selected regions of space, and at the continuum level elsewhere. It is derived…
The advent of robust, reliable and accurate higher order Godunov schemes for many of the systems of equations of interest in computational astrophysics has made it important to understand how to solve them in multi-scale fashion. This is so…
The Primal-Dual hybrid gradient (PDHG) method is a powerful optimization scheme that breaks complex problems into simple sub-steps. Unfortunately, PDHG methods require the user to choose stepsize parameters, and the speed of convergence is…
We have carried out numerical simulations of strongly gravitating systems based on the Einstein equations coupled to the relativistic hydrodynamic equations using adaptive mesh refinement (AMR) techniques. We show AMR simulations of NS…
Simulations with high accuracy are an essential part of scientific research to accelerate the innovation process. They are especially useful for finding novel approaches or optimizing existing methods. Today, powerful software tools are…
Recent advancements in deep learning optimization have introduced new algorithms, such as Schedule-Free optimizers, AdEMAMix, MARS and Lion which modify traditional momentum mechanisms. In a separate line of work, theoretical acceleration…
Learning accurate numerical constants when developing algebraic models is a known challenge for evolutionary algorithms, such as Gene Expression Programming (GEP). This paper introduces the concept of adaptive symbols to the GEP framework…
We present a scalable, parallel implementation of a solver for the solution of a phase-field model for quasi-static brittle fracture. The code is available as open source. Numerical solutions in 2d and 3d with adaptive mesh refinement show…
Simulating space plasma in a global scale is computationally demanding. Modeling different regions with different resolution can save computational resources without compromising too much on simulation accuracy. This thesis examines…
The linear model uses the space defined by the input to project the target or desired signal and find the optimal set of model parameters. When the problem is nonlinear, the adaption requires nonlinear models for good performance, but it…
In this paper, we propose an adaptive keyframe selection method for improved 3D scene reconstruction in dynamic environments. The proposed method integrates two complementary modules: an error-based selection module utilizing photometric…
Sparse Matrix-Matrix Multiplication (SpMM) is a fundamental computation in graph analytics, scientific simulation, and sparse deep learning workloads. However, the extreme irregularity of real-world sparse matrices prevents existing…
Learning dexterous and agile policy for humanoid and dexterous hand control requires large-scale demonstrations, but collecting robot-specific data is prohibitively expensive. In contrast, abundant human motion data is readily available…
Adaptive representations are increasingly indispensable for reducing the in-memory and on-disk footprints of large-scale data. Usual solutions are designed broadly along two themes: reducing data precision, e.g., through compression, or…
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…
We present a novel algorithm to compute multi-scale curvature fields on triangle meshes. Our algorithm is based on finding robust mean curvatures using the ball neighborhood, where the radius of a ball corresponds to the scale of the…
We present a scalable combinatorial algorithm for globally optimizing over the space of geometrically consistent mappings between 3D shapes. We use the mathematically elegant formalism proposed by Windheuser et al. (ICCV 2011) where 3D…
Model-based reinforcement learning is a powerful tool, but collecting data to fit an accurate model of the system can be costly. Exploring an unknown environment in a sample-efficient manner is hence of great importance. However, the…