Next-Generation Design and Simulation with SplitFXM
The end-to-end platform for physics-aware AI to build smarter digital twins and faster industrial simulations.
Powerful Features
SplitFXM provides a comprehensive toolkit for building robust digital twins and high-fidelity simulation workflows.
Scientific Machine Learning
Use the latest architectures (DeepONets, FNOs, World Models, etc.) and efficient training techniques to build cost-efficient, physical AI models.
Ultra-High Precision
Achieve extreme accuracy in simulations with high-order numerical methods (Discontinuous Galerkin, Finite Element and Volume).
State-of-the-art Optimization Solvers
Robust approaches for solutions of highly stiff, non-linear models (using Block/Split Newton methods).
Universal Performance
High-performance parallel execution across hardware, from standard CPUs to NVIDIA and AMD GPUs.
Extreme Event Tracking
Capture sudden changes like shockwaves using advanced numerical methods (WENO/TENO schemes).
Real-World Flexibility
Adapts to complex, irregular shapes and real-world boundaries that standard simulation tools struggle with.
Adaptive Mesh Refinement
Dynamically adjusts the computational grid to focus resources where they're needed most.
Scientific Machine Learning
With the right metrics, we ensure training meets theoretical bounds and minimize compute wastage
Latest in Physical AI - World Models support
Watch our masterclass:
Mathematical Techniques for Scientific Machine Learning
Solver Comparison
How SplitFXM differs from traditional boundary value problem solvers?
SciPy's solve_bvp and Julia's DifferentialEquations.jl
Requires transformation of higher-order differential equations into first-order systems:
# Must convert to dy/dx = f(x,y,p) form
# Original equation: y'' + p*y' + q*y = g(x)
# Converted system:
# y1' = y2
# y2' = g(x) - q*y1 - p*y2Explicit Jacobian matrices must be provided for large-scale simulation problems:
# Must define df/dy and df/dp manually
# This becomes increasingly tedious for large systemsSplitFXM Approach
Work directly with governing equations in their natural form:
# Define equations as they appear in physics/engineering
# No need to transform to first-order systems
# res = d2x(y) + p*dx(y) + q*y - g(x)Sparse Jacobians at runtime - Enhanced performance for large-scale digital twins
Comparison
For the Blasius Problem (ηmax = 10, N = 100)
| Method | Time (s) |
|---|---|
| SplitFXM++ | ~0.065 |
| SciPy solve_bvp (no Jacobian) | ~0.073 |
By focusing on the natural form of equations, SplitFXM makes it more intuitive and accessible while providing computational efficiency.
The “Split” Methodology
Our unique approach divides complex systems into multiple variable segments for more efficient computation.
1. System Division
Break down complex physical systems into manageable subsystems.
2. Variable Fixing
Hold some variables fixed while solving for others in each subsystem.
3. Iterative Solution
Alternate between subsystem solutions, gradually converging to the complete system solution.
4. Recursive Processing
Apply the same approach recursively for highly complex systems.
The “Split” Ecosystem
Our comprehensive suite of solvers for advanced simulation and digital twin challenges
“Divide and conquer for complex numerical solutions”
SplitNewton++
Core Split-Newton Solver for efficient non-linear system resolution.
SplitContin++: Numerical Continuation solver
Enables arc-length and one-point control for any arbitrary variable, essential for tracking solution branches.
SplitDAE++: General Differential-Algebraic Equation (DAE) Solver
Supports classic and advanced numerical integration schemes like Backward Differentiation Formulas (BDF) and Euler methods.
SplitOPS++: Operator-Splitting framework for DAEs
Implements various splitting schemes including Lie, Strang, and higher-order Suzuki methods for increased accuracy and stability in coupled systems.
SplitFXM++
The dedicated Multi-dimensional Boundary Value Problem (BVP) Solver, acting as the core integration engine. Architecture-independent parallelization across CPU and GPU (NVIDIA/AMD).
Python Side
SplitNewton & SplitFXM
Python implementations of the Split-Newton Solver and 1D BVP Solver.
Watch SplitFXM++ in Action
See how SplitFXM++ handles complex real-world simulations with extreme accuracy and speed.
Application Layer
High-fidelity solvers built on the SplitFXM core, excelling at Aerospace, Energy, Next-Gen Batteries, Thermal Management, and Industrial Chemistry.
ShockFXM++
Advanced Shock-Tube Simulator for analyzing wave propagation and discontinuities.
FlameletFXM++
Flamelet Solver specialized for combustion modeling in mixture-fraction space, vital for non-premixed flame analysis.
DropletFXM++
High-fidelity multicomponent droplet evaporation simulations.
- Spherical, transient, liquid-phase heat and species diffusion
- Gas-phase transport via Cantera
- VLE modeled via Raoult’s Law
MultiphaseFXM++
High-fidelity multiphase solver for complex fluid interfaces.
- Advanced VOF with NVD schemes
- High-order Level-Set methods
HypeSuite
Hypersonic Flow Calculation Suite based on SplitFXM. A comprehensive application featuring:
- Atmosphere models and trajectory
- Inviscid/Viscous shock relations
- Real gas thermodynamics
- Hypersonic vehicle design
Pricing
Simple and transparent licensing options
| License Type | Price | Intended Use | Action |
|---|---|---|---|
| Non-Commercial | Free | Research, educational, and personal use* | Download |
| Commercial | On Request | Business purposes or revenue-generating use | Request |
| C++ Version (including pre-requisites)** | On Request | For all purposes | Request |
*Free version supports 1D only with limited numerical schemes
**For an example application, see ShockFXM++
Non-commercial use is licensed under Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)
Have questions? Contact us
Citing SplitFXM
If you use SplitFXM in your research, please cite it using the following format:
@software{pavan_b_govindaraju_2025_14827049,
author = {Pavan B Govindaraju},
title = {gpavanb1/SplitFXM: v0.5.0},
month = feb,
year = 2025,
publisher = {Zenodo},
version = {v0.5.0},
doi = {10.5281/zenodo.14827049},
url = {https://doi.org/10.5281/zenodo.14827049},
}SplitFXM is an open-source project. Your acknowledgment helps support its continued development.