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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

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5 results for “Dirac-Frenkel”

A Dirac-Frenkel-Onsager principle: Instantaneous residual minimization with gauge momentum for nonlinear parametrizations of PDE solutionscs.LG

A new principle minimizes residual and introduces momentum to improve PDE solution dynamics.

problem Ill-conditioning in Dirac-Frenkel residual minimization leads to non-unique parameter dynamics.

method Introduces a history variable (momentum) to select better-conditioned parameter velocities, preserving residual minimization while promoting smooth parameter evolutions.

result The approach leads to increased robustness in singular and near-singular PDE solution regimes.

Dirac-Frenkel PDE solutions residual minimization gauge freedom momentum

2026-04-30abs ↗pdf ↗

Geometry of tree-based tensor formats in tensor Banach spacesmath.NA

Extends geometrical description of tensor manifolds in tree-based formats.

problem Geometrical description of tensor manifolds in tree-based formats.

method Provided a new geometrical description of manifolds of tensors in tree-based format.

result Geometrical description compatible with Tucker format.

tensor formats tree-based tensor networks manifolds tensor Banach spaces

2020-11-17abs ↗pdf ↗

On the Dirac-Frenkel Variational Principle on Tensor Banach Spacesmath.NA

The main goal of this paper is to extend the so-called Dirac-Frenkel Variational Principle in the framework of tensor Banach spaces. To this end we observe that a tensor product of normed spaces can be described as a union of disjoint connected components. Then we show that each of these connected components, composed …

2016-10-31abs ↗pdf ↗

Neural Galerkin Schemes with Active Learning for High-Dimensional Evolution Equationsmath.NA

Neural Galerkin schemes use active learning to solve high-dimensional equations.

problem Inaccurate function approximations in high dimensions with limited training data.

method Neural Galerkin schemes based on deep learning with active learning for high-dimensional PDEs.

result Active data collection improves the numerical solution of high-dimensional equations.

Neural Galerkin Active Learning High-Dimensional PDEs Partial Differential Equations Deep Learning

2022-03-02abs ↗pdf ↗

Geometric Structures in Tensor Representations (Final Release)math.NA

The main goal of this paper is to study the geometric structures associated with the representation of tensors in subspace based formats. To do this we use a property of the so-called minimal subspaces which allows us to describe the tensor representation by means of a rooted tree. By using the tree structure and the d…

2015-05-12abs ↗pdf ↗