Dilay Gedik
Inverse Problems / Engineering Optimization

Inverse Modeling & Optimization Laboratory

Inverse Problems, Parameter Identification and Engineering Design

A scientific computing platform for estimating physical parameters, calibrating mathematical models, optimizing constrained designs and quantifying uncertainty.

Open application

Engineering problem

Inverse Modeling & Optimization Laboratory is a scientific computing platform for estimating physical parameters from observations, calibrating mathematical models, optimizing constrained engineering designs and quantifying uncertainty. It asks the inverse question: given measured system behavior, which physical parameters could have produced it?

Mathematical foundations

Parameter identification

A regularized weighted least-squares problem can be written as

θ∗=arg⁡min⁡θ[∑iwi(yi−f(xi,θ))2+λR(θ)].\boldsymbol\theta^*=\arg\min_{\boldsymbol\theta}\left[\sum_i w_i\left(y_i-f(x_i,\boldsymbol\theta)\right)^2+\lambda R(\boldsymbol\theta)\right].

Here, yiy_i are observations, f(xi,θ)f(x_i,\boldsymbol\theta) is the model prediction, wiw_i weights residuals and RR regularizes poorly constrained parameter combinations.

Optimization methods

The platform uses bounded nonlinear least squares for local, gradient-informed calibration and differential evolution for population-based global search. Comparing the two makes it possible to examine convergence, initialization sensitivity and the presence of competing parameter regions.

Sensitivity and identifiability

Numerical Jacobians support local sensitivity analysis. Matrix rank, conditioning and parameter correlations help distinguish a low residual from a uniquely identifiable parameter set. A close fit alone does not prove that the inferred parameters are unique.

Uncertainty quantification

Local covariance approximations and bootstrap confidence intervals provide limited uncertainty estimates. The current scope does not claim full Bayesian inference or comprehensive global sensitivity analysis.

Implemented model families

Thermal system identification

Newtonian cooling uses

T(t)=Tambient+(Tinitial−Tambient)e−ktT(t)=T_{ambient}+(T_{initial}-T_{ambient})e^{-kt}

to infer thermal parameters from temperature observations.

Structural vibration calibration

Dynamic-response observations can be used to identify supported stiffness and damping parameters within the implemented structural model.

Biomedical transport calibration

A simplified two-compartment transport model provides concentration data for parameter-estimation experiments. It is a computational demonstration, not a clinically validated biomedical model.

Constrained design optimization

Beam, thermal or cooling-system and vibration-isolation studies define objective functions, constraints and feasible regions. Solver output includes convergence and feasibility diagnostics rather than only a nominal optimum.

Computational capabilities

  • CSV measurement import and synthetic benchmark datasets
  • Fitted-versus-observed plots and residual analysis
  • Regularization studies and numerical Jacobians
  • Bootstrap intervals
  • Design-space visualization and feasibility diagnostics
  • JSON result export and Markdown technical reports

Verification and limitations

Synthetic benchmarks with known parameters are used to inspect estimator behavior, residual structure and recovery error. Results depend on model adequacy, data quality, parameter bounds and identifiability. Synthetic demonstrations do not establish experimental or clinical validation.

Engineering applications

The laboratory supports model calibration, parameter estimation, uncertainty analysis, constrained optimization and simulation-driven engineering design.

Technical resources

The deployment at optimization.hemaeoslabs.com was verified before being listed here. No public source repository is presented.