Enum InverseProblemRegularization

Namespace

AiDotNet.PhysicsInformed.Interfaces

Assembly

AiDotNet.dll

Specifies the type of regularization for inverse problems.

public enum InverseProblemRegularization

Fields

Bayesian = 5

Bayesian regularization using prior distributions.

Treats parameters as random variables with prior distributions. Uses maximum a posteriori (MAP) estimation. Good when: Have prior knowledge about parameter distributions

ElasticNet = 4

Elastic Net: Combination of L1 and L2.

Adds term: λ₁ * Σᵢ |pᵢ| + λ₂ * Σᵢ (pᵢ)² Effect: Sparse parameters with controlled magnitudes Good when: Want benefits of both L1 and L2

L1Lasso = 2

L1 (Lasso) regularization: Prefers sparse parameters.

Adds term: λ * Σᵢ |pᵢ| Effect: Encourages some parameters to be exactly zero Good when: Only few parameters are actually relevant

L2Tikhonov = 1

L2 (Tikhonov) regularization: Prefers small parameter values.

Adds term: λ * Σᵢ (pᵢ)² Effect: Pulls parameters toward zero Good when: Expected parameters are small

None = 0

No regularization (may be unstable).

TotalVariation = 3

Total Variation regularization: Prefers smooth parameter fields.

Adds term: λ * ∫|∇p| Effect: Encourages piecewise constant parameter distributions Good when: Parameter is spatially varying but piecewise constant