Proposes EDESH-SA for better inventory management under uncertainty.
problem Inventory management under uncertainty.
method Ensemble Differential Evolution with simulation-based hybridization and self-adaptation.
result Improves financial performance and optimizes search spaces.
A new method evolves point clouds using B-splines for smooth surfaces.
problem Evolution of smooth surfaces from discrete point clouds.
method Adaptive Lagrangian B-spline framework for geometric evolution.
result Efficient and accurate reproduction of surface evolution phenomena.
Algorithm improves vanilla option pricing accuracy during and before COVID-19.
problem Improving vanilla option pricing accuracy during and before the pandemic.
method Combinational Mutation Strategy of Differential Evolution (CmDE) algorithm for bi-objective optimization.
result Algorithm approximates real market vanilla option prices more accurately than Black-Scholes.
Gradients help find global optima in complex functions.
problem Finding global optima in functions with many local minima.
method A principle for generating search directions from non-local quadratic approximants based on gradients.
result The proposed algorithm and CMA-ES perform better than random reinitialized BFGS.
Proposes ECS-DBN for cost-sensitive deep belief network in imbalanced classification.
problem Imbalanced data classification with unequal misclassification costs.
method ECS-DBN uses adaptive differential evolution to optimize misclassification costs based on training data.
result ECS-DBN consistently outperforms state-of-the-art methods on benchmark and real-world datasets.
Differential Evolution outperforms SMAC in hyperparameter tuning.
problem Automated hyperparameter tuning for machine learning.
method Empirical study comparing Differential Evolution to SMAC.
result Differential Evolution outperforms SMAC on most datasets.
CoLoRA models predict PDE solutions quickly and accurately with minimal data.
problem Efficiently modeling PDE solutions with limited data.
method Continuous low-rank adaptation of neural networks trained on offline data.
result Predictions are orders of magnitude faster and more accurate than classical methods.
Study nondifferentiable metrics in general relativity, resolving causality issues and limits evolution scenarios.
problem Causality issues and evolution scenarios in black hole interiors with closed timelike geodesics.
method Method of equivalence on Courant algebroids to derive new differential invariants.
result Resolved causality issues and limited evolution scenarios for gravitational collapse.
ANODEV2 extends Neural ODEs to include evolving parameters.
problem Training and accuracy of neural networks.
method Coupled ODE-based framework for evolving neural network parameters.
result ANODEV2 achieves higher accuracy than baseline models and Neural ODEs.
Study evolutes of curves with varying smoothness.
problem Understanding evolutes of curves with low smoothness.
method Analyzing the relationship between curve smoothness and evolute regularity.
result Evolutes have one less order of smoothness than the parent curve in generic cases.
The paper proves differentiability of evolution maps in Lie groups.
problem Differentiability of evolution maps in infinite-dimensional Lie groups.
method Showed sequential continuity (Mackey k-continuity) leading to differentiability.
result Differentiability of evolution maps in Ck-semiregular Lie groups. Solvable structures are exploited in order to find families of explicit solutions to evolution PDEs admitting suitable differential constraints. The effectiveness of the method is verified on several explicit examples.
The paper explores quaternionic curves using differential geometry.
problem Understanding quaternionic curves.
method Differential geometry applied to quaternionic curves.
result Simpler formulations of quaternionic curves.
Differentiable NAS frameworks grow networks wider and deeper, revealing biases in wiring evolution.
problem Understanding the evolution of neural architecture wiring in differentiable NAS methods.
method Unified view on searching algorithms, local cost minimization, empirical and theoretical analyses.
result Implicit inductive biases cause observed searching patterns in differentiable NAS methods.
Global calculus for manifolds with boundary, solving evolution problems.
problem Global solvability of evolution problems on manifolds with boundary.
method Established global functional calculus and Gårding inequality for pseudo-differential operators without local coordinates.
result Global solvability for a class of evolution problems.
Study on focal surfaces and evolutes of framed curves in hyperbolic 3-space using Legendrian duality.
problem Investigate differential geometry properties of framed curves, including singular points.
method Use Legendrian dualities to analyze focal surfaces and evolutes of hyperbolic framed curves.
result Show the relationship among focal surfaces, evolutes, and dual surfaces of evolutes.
New deep learning method approximates Benes filter model.
problem Approximating high-dimensional SPDEs for filtering.
method Deep learning mesh-free neural network representation.
result First study of neural network method for Benes model.
Quantum-enhanced metrology aims to estimate an unknown parameter such that the precision scales better than the shot-noise bound. Single-shot adaptive quantum-enhanced metrology (AQEM) is a promising approach that uses feedback to tweak the quantum process according to previous measurement outcomes. Techniques and form…
Deep learning approximates PDE evolution operators from solution data.
problem Recovering unknown time-dependent PDEs from solution data.
method Approximate evolution operator in modal space, train deep neural network.
result Deep learning method accurately approximates PDE solutions.
Using the result by D.Gessler (Differential Geom. Appl. 7 (1997) 303-324, DIPS-9/98, http://diffiety.ac.ru/preprint/98/09_98abs.htm), we show that any invariant variational bivector (resp., variational 2-form) on an evolution equation with nondegenerate right-hand side is Hamiltonian (resp., symplectic).
Backlund transformations are used to search for solutions, particularly soliton solutions, of non-linear differential equations. In this paper we present an invariant geometrical theory of Backlund transformations for second order evolution equations with one space variable. The main concept is that of connection defin…
New formula simplifies evolution of twist knots and calculates Racah matrices for rectangular representations.
problem Simplifying evolution of twist knots and calculating Racah matrices for rectangular representations.
method Developed a universal formula for triangular evolution matrix B applicable to rectangular representations R=[rs]. Used skew characters and Macdonald polynomials. result Explicit knowledge of twist-family evolution leads to a nearly explicit answer for Racah matrix Sˉ in arbitrary rectangular representation R. ES-MAML uses Evolution Strategies for MAML, avoiding second derivative estimation.
problem Solving the MAML problem with efficient second derivative estimation.
method Applies Evolution Strategies to MAML, avoiding second derivative estimation.
result ES-MAML performs competitively and often better with fewer queries.
The aim of this paper is to adapt the general multitime maximum principle to a Riemannian setting. More precisely, we intend to study geometric optimal control problems constrained by the metric compatibility evolution PDE system; the evolution ("multitime") variables are the local coordinates on a Riemannian manifold,…
Enhances inverse design optimization with machine learning and reduced fidelity simulations.
problem Limited compute resources in inverse design optimization.
method Synergy of multi-fidelity simulations, machine learning, and search space reduction.
result Significant computational resource savings and improved optimization performance.
New method uses randomized sparse neural networks to solve time-dependent PDEs more accurately and efficiently.
problem Numerical challenges in training neural networks sequentially in time to solve time-dependent PDEs.
method Introduces Neural Galerkin schemes that update randomized sparse subsets of network parameters at each time step.
result Up to two orders of magnitude more accurate and two orders of magnitude faster than dense update schemes.
A novel meta-learning method using ES for efficient reinforcement learning.
problem Sample inefficiency in reinforcement learning.
method Evolution strategies (ES) for exploration in parameter space, deterministic policy gradients for adaptation.
result Demonstrates improved performance in high-dimensional control tasks compared to gradient-based methods.
The paper classifies different types of cusps on plane curves.
problem Investigating various types of cusps on plane curves.
method Examining criteria for (n,n+1) cusps with differential conditions and relations to evolutes of fronts. result Complete classifications for (4,5)-cusps. Study torsion parallel spinors on Lorentzian 4-manifolds and their evolution flows.
problem Investigate torsion parallel spinors on Lorentzian four-manifolds.
method Geometric study via spinorial polyforms and supersymmetric NS-NS system.
result Globally hyperbolic evolution flow determined by supersymmetric solutions.
ES for non-differentiable parameters scales to large models.
problem Learning non-differentiable parameters in large models.
method Hybrid approach combining ES for non-differentiable and gradient-based methods for differentiable parameters.
result Hybrid approach is competitive and allows training sparse models from the start.
Deep learning improves evolutionary algorithms' adaptability.
problem Improving evolutionary algorithms' adaptability to various circumstances.
method Using deep reinforcement learning to dynamically adjust evolutionary algorithms' strategies.
result Deep learning enhances evolutionary algorithms' fitness increase and attainable fitness.
A fundamental question in Riemannian geometry is to find canonical metrics on a given smooth manifold. In the 1980s, R. Hamilton proposed an approach to this question based on parabolic partial differential equations. The goal is to start from a given initial metric and deform it to a canonical metric by means of an ev…
Modern treatment of space curve evolutes and involutes.
problem Understanding space curve evolutes and involutes.
method Unified treatment with novel observations and computer graphics.
result Illustration of space curve evolutes and involutes with computer graphics.
A variational proof is provided of the existence and uniqueness of evolutions of regular Lagrangian systems.
This tutorial introduces the CMA Evolution Strategy (ES), where CMA stands for Covariance Matrix Adaptation. The CMA-ES is a stochastic, or randomized, method for real-parameter (continuous domain) optimization of non-linear, non-convex functions. We try to motivate and derive the algorithm from intuitive concepts and …
Introduces a new stochastic optimization method for deep learning.
problem Minimizing loss functions in deep neural networks.
method Introduces a second-order stochastic Runge-Kutta method and an adaptive SGD-G2.
result The method yields consistent minimization of loss functions and automatically adjusts learning rates.
This paper gives two methods for constructing associative 3-folds in R^7, based around the fundamental idea of evolution equations, and uses these methods to construct examples of these geometric objects. The paper is a generalisation of the work by Joyce in math.DG/0008021, math.DG/0008155, math.DG/0010036 and math.DG…
This paper integrates Kelly's Criterion into portfolio optimization models.
problem Incorporating Kelly's Criterion into standard portfolio optimization models.
method Developed a model combining risk and return, solved using differential evolution algorithm.
result Evolutionary algorithms can solve portfolio optimization problems with Kelly's Criterion.
We study the problem to provide a triangular form based on implicit differential equations for non-linear multi-input systems with respect to the flatness property. Furthermore, we suggest a constructive method for the transformation of a given system into that special triangular shape, if possible. The well known Brun…
Develops finite-gap solutions for Pohlmeyer--Lund--Regge equation and Lund--Regge curve evolution.
problem Solving the Pohlmeyer--Lund--Regge equation and understanding Lund--Regge curve evolution.
method Finite-gap construction using hyperelliptic spectral data, Baker--Akhiezer function, and SU(2)-frame. result Explicit theta-quotient formula for PLR solutions and criteria for Lund--Regge curve evolution.
We study the evolution of convex complete non-compact graphs by positive powers of Gauss curvature. We show that if the initial complete graph has a local uniform convexity, then the graph evolves by any positive power of Gauss curvature for all time. In particular, the initial graph is not necessarily differentiable.
We perform a classification of the Lie point symmetries for the Black--Scholes--Merton Model for European options with stochastic volatility, σ, in which the last is defined by a stochastic differential equation with an Orstein--Uhlenbeck term. In this model, the value of the option is given by a linear (1 + 2) evolu…
A model is presented of the market dynamics to emphasis the effects of increasing returns to scale, including the description of the born and death of the adaptive producers. The evolution of market structure and its behavior with the technological shocks are discussed. Its dynamics is in good agreement with some empir…
Lectures on surface evolution through singularities.
problem Analyzing the mean curvature flow of surfaces and their singularities.
method Analysis of neck and conical singularities, using monotonicity formulas, epsilon-regularity, weak solutions, and blowup techniques.
result Unique evolution through neck singularities, nonuniqueness through conical singularities.
Defect of knot polynomials remains invariant under certain braid substitutions.
problem Invariance of knot polynomial defects under specific transformations.
method Investigation of defect invariants under antiparallel and parallel braid substitutions.
result Defect remains unchanged under antiparallel braid substitutions and changes by half the added length under parallel braid substitutions.
Global anchor method detects language shifts and domain adaptation.
problem Detecting corpus-level language shifts and domain adaptation.
method Global anchor method for comparing word embeddings.
result Global anchor method is superior to alignment method in applicability and implementation.
We prove that the Kupershmidt deformation of a bi-Hamiltonian system is itself bi-Hamiltonian. Moreover, Magri hierarchies of the initial system give rise to Magri hierarchies of Kupershmidt deformations as well. Since Kupershmidt deformations are not written in evolution form, we start with an outline a geometric fram…
This paper describes the evolution of aspects of differential and algebraic gometry from the mid 17th century till the end of the 18th century.