Compressible and high-speed flow
Steady internal and external flows, nozzles, intakes and shock-containing regimes are primary research targets.
NeuralFlowML Graph Neural Operator CFD solver
A learned solver trained directly from CFD numerics
NeuralFlowML is LIKUA's Graph Neural Operator CFD solver. Instead of learning from reference flow fields, it learns iterative flow-state updates from the finite-volume residuals, numerical fluxes, discrete Jacobians and boundary-condition treatment used by NeuralFlow.
No reference solution datasetThe learning signal comes from the discrete numerical method and the generated rollout itself.
No reference fieldsNo labeled CFD solutions or teacher trajectories are required during training.
Finite-volume objectiveMass, momentum and energy imbalance provide the physical training signal.
Discrete sensitivitiesSolver Jacobians and automatic differentiation propagate numerical feedback.
Graph solver updateThe GNO advances primitive flow variables on the unstructured computational graph.
How training works
The solver provides the training signal
NeuralFlowML begins from a valid initial state and generates its own rollout. NeuralFlow evaluates each generated state with the same discrete conservation equations, boundary treatment and sensitivities used by the CFD solver.
Learning to solve, not to imitate a solution
The Graph Neural Operator produces successive corrections to velocity, pressure and temperature. There is no converged target field to reproduce.
Training is driven by how well the generated state satisfies the discrete numerical system, so the learned operator is coupled directly to the finite-volume formulation.
Initialize the CFD problemGeometry, mesh, initial conditions and boundary conditions define the starting graph state.
Advance with the GNOThe operator generates the next primitive-variable correction on the computational graph.
Evaluate discrete conservationFinite-volume fluxes, sources and boundary numerics measure the quality of the generated state.
Backpropagate solver feedbackDiscrete Jacobians and automatic differentiation train the operator through its generated rollout.
Solver-native training: no supervised CFD field dataset, prescribed teacher trajectory or reference solution is used. Independent validation against accepted CFD benchmarks and experiments remains required.
Current graph statemesh, flow variables and boundary data
→
GNO updatelearned solver iteration
Discrete sensitivitiesJacobians and automatic differentiation
←
Finite-volume evaluationresiduals, fluxes, sources and BC treatment
The next training update is produced by the numerical quality of the state generated by the GNO itself.
Research focus
Designed for difficult conservative flow problems
The research program targets regimes where pointwise surrogate models are least convincing: conservation-dominated flow, strong gradients, unstructured meshes and boundary-sensitive solutions.
Unstructured, boundary-sensitive problems
The operator acts on mesh connectivity and geometric features while retaining wall and characteristic-boundary information.
Extensions under study
Transient, turbulent, scale-resolving and multiphysics applications remain research-roadmap items requiring dedicated validation.
Development status
Implemented research and remaining validation are separated explicitly
NeuralFlowML remains an active R&D program. Claims on speed, robustness and generalization will be tied to controlled benchmark evidence, and training without reference data does not remove the need for independent verification.
Implemented foundations
- Training without example or reference CFD fields
- Graph Neural Operator updates of primitive flow variables
- Finite-volume residuals, fluxes, sources and boundary numerics as the objective
- Solver-computed discrete flux Jacobians and forward-mode automatic differentiation
- Reverse-mode training through generated multi-rollout trajectories
- In-solver C++ training and execution pathway
Work still required
- Benchmark-based speed, accuracy and robustness qualification
- Generalization across geometries, meshes and operating conditions
- Stable training over wider initial-condition ranges
- Large three-dimensional model and memory scaling
- Turbulent, transient and multiphysics validation
- Failure detection and fallback to the validated CFD solver
LIKUA simulation stack
Validated physics, learned solver research and operational workflows
NeuralFlowML is the Graph Neural Operator research layer of LIKUA's engineering platform. Its parameters are trained from solver numerics rather than from example CFD solutions.
Research contact
Graph Neural Operator CFD research and validation
LIKUA is open to technically grounded collaboration on benchmark design, solver-native learning, Graph Neural Operator development and validation for demanding aerospace and industrial flow problems.
Contact