Existence and uniqueness of weak entropy solutions for nonlocal nonlinear scalar conservation laws is proven on short time horizons via fixed-point methods, extending to any finite horizon under additional assumptions.
Finite Volume Methods for Hyperbolic Problems
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Duality on operator Frobenius algebras solves the Eisenhart-Stäckel problem by classifying all nondegenerate finite-dimensional integrable systems with quadratic integrals where the associated (1,1)-tensors commute.
Defines resilience evaluation D^ρ π as the L1-limit of scaled dynamic risk measure applied to process increments, and derives its dual representation as worst-case conditional expectation of an effective drift when ρ arises from BSDEs with Lipschitz or quadratic drivers.
PI-MFA optimizes tensor-product B-spline control points to balance data fidelity against PDE residuals, producing physically consistent continuous flow fields.
A latent-space reduced-order model using autoencoders and learned dynamics enables Bayesian recovery of initial density and pressure in Sod shock tube simulations, with posterior uncertainty contracting substantially as observation density increases.
Introduces Hodge Spectral Duality, a hybrid neural architecture that applies Hodge orthogonality and operator splitting to isolate unlearnable topological degrees of freedom from learnable geometric dynamics in solution operators on geometric meshes.
amerta is a new Python library that implements and verifies a standard finite-volume solver for four canonical 1D dam-break Riemann problems against analytical solutions.
citing papers explorer
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Existence and uniqueness of nonlocal nonlinear conservation laws via fixed-point methods
Existence and uniqueness of weak entropy solutions for nonlocal nonlinear scalar conservation laws is proven on short time horizons via fixed-point methods, extending to any finite horizon under additional assumptions.
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Duality of operator Frobenius algebras and solution of Eisenhart-St\"ackel problem in the non-diagonal case
Duality on operator Frobenius algebras solves the Eisenhart-Stäckel problem by classifying all nondegenerate finite-dimensional integrable systems with quadratic integrals where the associated (1,1)-tensors commute.
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Financial Resilience Evaluation: From Conditional Expectations to Dynamic Convex Risk Measures
Defines resilience evaluation D^ρ π as the L1-limit of scaled dynamic risk measure applied to process increments, and derives its dual representation as worst-case conditional expectation of an effective drift when ρ arises from BSDEs with Lipschitz or quadratic drivers.
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A Physics-Informed B-Spline Framework for Continuous Approximation of Flow Data
PI-MFA optimizes tensor-product B-spline control points to balance data fidelity against PDE residuals, producing physically consistent continuous flow fields.
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The impact of observation density on Bayesian inversion of latent dynamics in shock-dominated flows
A latent-space reduced-order model using autoencoders and learned dynamics enables Bayesian recovery of initial density and pressure in Sod shock tube simulations, with posterior uncertainty contracting substantially as observation density increases.
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Topology-Preserving Neural Operator Learning via Hodge Decomposition
Introduces Hodge Spectral Duality, a hybrid neural architecture that applies Hodge orthogonality and operator splitting to isolate unlearnable topological degrees of freedom from learnable geometric dynamics in solution operators on geometric meshes.
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amerta: A Python Library for Idealized 1D Saint--Venant Dam-Break Simulation
amerta is a new Python library that implements and verifies a standard finite-volume solver for four canonical 1D dam-break Riemann problems against analytical solutions.