@modelscript/simulate

ModelScript Numerical Simulation, Continuum Physics, Surrogate Modeling & Operational Digital Twin Engine — explicit and stiff implicit ODE/DAE integrators, SUNDIALS (cvode/ida) WASM solvers, WebGPU batched WGSL compute execution, hybrid adjoint sensitivity with saltation matrices, 3D continuum FEA & Lattice Boltzmann CFD solvers, reduced-order surrogate modeling, Monte Carlo / Sobol uncertainty quantification, and real-time state estimation.

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Architecture & Capabilities

1. Explicit & Implicit ODE / DAE Numerical Solvers (@modelscript/simulate/solvers, src/core/)

Operates directly on @modelscript/runtime linear-memory DAEBuilder arenas (simulateArena, simulateArenaAsync, WasmSimulationRunner):

• Explicit Runge-Kutta Integrators:
  • euler: Fixed-step forward Euler stepper.
  • rk4: Classical 4th-order Runge-Kutta integrator.
  • dopri5: Dormand-Prince 5(4) adaptive step-size integrator with dense 4th-order Hermite interpolation and zero-crossing event location.
  • tsit5 (src/solvers/tsit5.ts): Tsitouras 5(4) adaptive Runge-Kutta method optimized for non-stiff continuous dynamics.
• Stiff Implicit & Rosenbrock ODE / DAE Integrators:
  • trbdf2 (src/solvers/trbdf2.ts): L-stable Trapezoidal Rule / 2nd-Order Backward Differentiation Formula composite method with adaptive step control.
  • rodas4p (src/solvers/rodas4p.ts): 4th-order stiffly accurate Rosenbrock-Wanner method for stiff ODEs and index-1 DAEs without nonlinear Newton iteration.
  • bdf: Variable-order (1–5), variable-step Backward Differentiation Formula solver with sparse KLU/CSR Jacobian factorization (src/solvers/sparse-solver-bridge.ts).
  • SUNDIALS WASM (cvode & ida, src/solvers/sundials-wasm.ts): WebAssembly-compiled Lawrence Livermore SUNDIALS CVODE (Adams-Moulton / BDF) and IDA (implicit differential-algebraic solver) with exact rootfinding.
• Specialized Solvers (src/solvers/): Delay Differential Equations (dde-solver.ts), Stochastic Differential Equations (sde-solver.ts, Euler-Maruyama / Milstein), Two-Point Boundary Value Problems (bvp-solver.ts, collocation/shooting), and Nodal Admittance Power Systems EMT (src/solvers/emt/).

2. WebGPU Batched WGSL Compute Engine (@modelscript/simulate/webgpu)

• Automated DAE-to-WGSL Compilation (src/core/wgsl-codegen.ts, src/core/wgsl-cache.ts): Compiles flattened arena equations directly into WebGPU Shading Language (@compute @workgroup_size(64)) shaders.
• Massive Parallel Parameter Sweeps (src/core/webgpu-simulation-runner.ts, src/core/vmap-arena.ts): Executes tens of thousands of parameter trajectories concurrently on the GPU (gpu-buffers.ts, webgpu-reduction.ts) with automatic fallback to multi-threaded WASM SIMD workers.

3. Hybrid Adjoint Sensitivity & Differentiable Simulation (src/core/, @modelscript/simulate/optimizer)

• Continuous & Hybrid Adjoint Solvers (src/core/adjoint-integrator.ts, src/core/dae-adjoint-solver.ts, src/core/hybrid-adjoint.ts):
  • Computes exact gradients $\nabla_{\theta} \mathcal{L}$ of trajectory loss functions with $O(1)$ memory cost scaling with respect to parameter count using cubic Hermite forward checkpointing (dense-checkpoint-tape.ts).
  • Discontinuity Jump Conditions: Evaluates exact saltation matrices across state-dependent when zero-crossings and hybrid mode switches so gradients remain mathematically exact across impacts and switching events.
  • GPU & Autograd Bridges: webgpu-adjoint-runner.ts for batched GPU adjoints and torch-autograd-bridge.ts for PyTorch integration.
• Signal Temporal Logic (STL) Falsification (src/core/stl_monitor.ts, src/core/falsification-runner.ts): Quantitative STL robustness semantics ($\rho(\varphi, \mathbf{x}, t)$) coupled with L-BFGS-B / CMA-ES optimization (src/optimizer/) for automated counterexample falsification.

4. PDE Method-of-Lines & 3D Continuum Physics (src/fea/, src/cfd/, @modelscript/simulate/meshing)

• 3D Finite Element Analysis (src/fea/):
  • FeaSolver (src/fea/fea-solver.ts): Linear and thermo-elastic static/modal 3D FEA solver supporting 4-node linear (Tet4Element) and 10-node quadratic (Tet10Element) tetrahedral elements, CalculiX .inp loading (inp-loader.ts), and von Mises stress recovery.
• 3D WebGPU Lattice Boltzmann CFD (src/cfd/):
  • WebGPULbmRunner (src/cfd/webgpu-lbm-runner.ts) & LBM_D3Q19_WGSL (src/cfd/shaders/lbm-d3q19.wgsl.ts): Hardware-accelerated 3D D3Q19 BGK/MRT Lattice Boltzmann fluid solver with LbmVoxelizer (lbm-voxelizer.ts), bounce-back obstacle boundaries, and aerodynamic drag/lift force integration.
• STEP B-Rep Mesher & Boundary Layer Extruder (src/meshing/):
  • step-mesher.ts, tet4-mesher.ts, boundary-layer-extruder.ts, patch-classifier.ts, and mesh-quality-analyzer.ts (dihedral angle, aspect ratio, Jacobian quality metrics).
• Multi-Physics FSI Coupling (src/core/multiphysics-port-coupler.ts, src/core/fsi-relaxation.ts, src/core/continuum-participant.ts): Couples 1D Modelica acausal ports with 3D FEA/CFD boundary patches.

5. Surrogate Modeling & Reduced-Order Models (src/surrogates/)

• Training Architectures (src/surrogates/rom-trainer.ts, src/surrogates/cfd-pod-surrogate.ts, src/surrogates/buckingham-pi.ts):
  • Multi-Layer Perceptrons (MLP), Polynomial Chaos Expansion (PCE) / multivariate polynomials, Radial Basis Functions (RBF), Proper Orthogonal Decomposition (POD) field surrogates, and dimensional Buckingham $\Pi$ group synthesis.
  • Out-of-Distribution Guardrails (src/surrogates/multivariate-bounds.ts): Convex-hull / Mahalanobis distance validity monitors.
• Multi-Format Export & Import (src/surrogates/modelica-surrogate-emitter.ts, src/surrogates/onnx-importer.ts): Exports trained surrogates to ONNX (.onnx), zero-dependency ANSI C99, and pure Modelica block (.mo) code; imports external .onnx graphs.

6. Uncertainty Quantification (@modelscript/simulate/uq) & Operational Digital Twin (@modelscript/simulate/twin, src/calibration/)

• Monte Carlo & Sobol Sensitivity (src/uq/monte-carlo.ts, src/uq/doe.ts): Latin Hypercube Sampling (LHS), Sobol quasi-random sequences, Saltelli first-order ($S_i$) and total-effect ($S_{Ti}$) variance-based sensitivity indices, and ensemble quantile envelopes.
• Operational Digital Twin Estimators (src/twin/, src/calibration/):
  • Moving Horizon Estimator (ArenaMHE, src/twin/arena-mhe.ts): Constrained sliding-window state and parameter trajectory estimation over live telemetry buffers (telemetry-buffer.js).
  • Unscented Kalman Filter (UnscentedKalmanFilter, src/calibration/unscented_kalman_filter.ts) & Virtual Sensor Fusion (virtual_sensor_fusion.ts): Nonlinear sigma-point state and unmeasured virtual sensor estimation.
  • Bayesian MCMC Calibration (BayesianCalibrator, src/calibration/bayesian_calibrator.ts): Affine-invariant ensemble / Metropolis-Hastings posterior parameter inference.
  • Drift Detection & RUL Prognostics (src/twin/drift-detector.ts, src/twin/prognostics.ts): Page-Hinkley / CUSUM parameter drift alarms and Remaining Useful Life (RUL) degradation horizon forecasting.

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Subpath Exports

Subpath	Description
@modelscript/simulate	Root barrel exporting all solvers, core runners, FEA, CFD, meshing, surrogates, UQ, calibration, and twin modules
@modelscript/simulate/core	simulateArena, WasmSimulationRunner, hybrid adjoints, STL monitors, and FSI couplers
@modelscript/simulate/solvers	tsit5, trbdf2, rodas4p, SUNDIALS cvode/ida, DDE, SDE, BVP, and EMT solvers
@modelscript/simulate/webgpu	WebGPUSimulationRunner and batched WGSL compute shaders
@modelscript/simulate/meshing	STEP B-Rep mesher, prism boundary layer extruder, and mesh quality analyzer
@modelscript/simulate/optimizer	L-BFGS-B, Nelder-Mead, CMA-ES, NSGA-II multi-objective optimizer, and parameter sweepers
@modelscript/simulate/uq	Monte Carlo runner, Sobol indices, and Design of Experiments (DoE)
@modelscript/simulate/twin	ArenaMHE, drift detector, RUL prognostics, and streaming telemetry ring buffers
@modelscript/simulate/jit	WebAssembly and JS JIT equation evaluator compilers

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Scripts

# Build TypeScript package
npm run build --workspace=@modelscript/simulate

# Run numerical solver, adjoint, FEA/CFD, surrogate, UQ, and digital twin tests
npm run test --workspace=@modelscript/simulate

# Typecheck and lint
npm run typecheck --workspace=@modelscript/simulate
npm run lint --workspace=@modelscript/simulate