AI Glossary
The complete dictionary of Artificial Intelligence
Model Order Reduction
Set of mathematical and computational techniques aimed at simplifying complex models while preserving their essential behavior and predictive accuracy under specified conditions.
Proper Orthogonal Decomposition
Dimensionality reduction method extracting the dominant modes of a dynamical system from experimental or simulated data to construct an optimal basis in the energetic sense.
Reduced Basis
Low-dimensional vector subspace generated from representative solutions of the full model, enabling efficient approximation of solutions for new parameters.
Low-Rank Approximation
Technique consisting in representing high-dimensional tensors or matrices by a linear combination of a few fundamental components, thus reducing computational complexity.
Intrinsic Manifold Methods
Nonlinear model reduction approaches modeling system dynamics as evolving on a low-dimensional differential manifold embedded in the full state space.
Variational Autoencoders
Generative neural network architecture learning a probabilistic latent representation of complex physical data for efficient compression and reconstruction.
Galerkin Projection
Method ensuring the orthogonality of the residual with respect to a test subspace, essential for preserving conservation and stability properties of reduced models.
Dynamic Mode Decomposition
Spatio-temporal decomposition technique identifying dominant oscillatory modes and their growth/decay rates, particularly effective for unstable systems.
Passivation Methods
Strategies preserving passivity properties during reduction, ensuring stability of coupled models and avoiding non-physical numerical artifacts.
Hybrid POD-Galerkin
Combination of proper orthogonal decomposition with Galerkin projection to build optimized reduced models exploiting both data and equation structure.
Physics-Informed Neural Networks
Neural architectures integrating conservation laws and governing equations as learning constraints to guarantee adherence to fundamental physical principles.
Krylov Subspaces
Iterative methods constructing reduced bases from sequences of vectors generated by repeated application of the system operator, optimal for algebraic problems.
Parametric Reduction
Generation of reduced models valid over an entire parameter space of geometric, physical, or initial conditions, enabling rapid exploration in design and optimization.
Self-Organizing Maps
Unsupervised neural networks creating a low-dimensional discrete topology preserving neighborhood relationships between system states for nonlinear reduction.
Reinforcement Learning for Reduction
Optimal approach where an agent learns to dynamically select the most appropriate reduction strategies according to the current system state and computational objectives.
Proper Generalized Decomposition Method
Variable separation technique approximating the multidimensional solution by products of one-dimensional functions, exponentially reducing complexity for high-dimensional problems.
Empirical Interpolation Method
Strategy enabling efficient evaluation of nonlinear terms in reduced models through selective interpolation at optimized points, preserving the structure of original operators.