Accelerating Simulation with Machine Learning: Lessons from a Vehicle Dynamics Thesis
Key Takeaways for Engineers and Engineering Leaders
- Machine learning (ML) can replicate high-fidelity simulation results with strong accuracy with results up to R² ≈ 0.99
- Surrogate models reduce simulation time from hours to seconds, enabling faster iteration
- Model selection matters: GRUs delivered the best balance of accuracy and training efficiency
- Inputs define success: ML models perform best when the causality of the system is given and relevant data is provided
- Different tools, different tasks: ML complements, not replaces, physics-based modeling
- Immediate applications: real-time analysis, design space exploration, and rapid optimization
Why Simulation Teams Are Looking to Machine Learning
Engineering teams today are balancing two competing demands: increasing system complexity and shrinking development timelines. High-fidelity simulation remains essential for accuracy and confidence, but its computational cost can slow iteration, limit design exploration, and delay critical decisions.
At Modelon, this challenge is particularly visible when working with demanding engineering organizations, including motorsport teams operating at the limits of performance. In these environments, small modeling inaccuracies can translate directly into real-world consequences.
This thesis explored a key question: Can machine learning complement physics-based simulation to accelerate workflows without sacrificing engineering rigor?
Rather than replacing equations and system models, machine learning offers a way to approximate complex relationships when guided by relevant data and system expertise.
Predicting Vehicle Loads from Real-World Telemetry
The thesis focused on predicting forces and torques on a race car over a full lap: critical variables for understanding braking, cornering, and overall vehicle stability. Using telemetry data from NASCAR racing, the team worked with:
- driver inputs such as throttle, brake, gear, and steering angle.
- measured signals including acceleration, orientation and position.
Because forces and torques were not directly measured, they were computed using a detailed vehicle dynamics model in Modelon Impact. These simulation results served as the “ground truth” for training machine learning models.
This setup reflects a common industry scenario: physics-based models provide trusted results, while data-driven approaches aim to replicate or accelerate them.
A Structured, Physics-Informed Approach to Machine Learning
While the racecars took sharp corners, the project itself used straightforward engineering practices. Rather than using machine learning as a black box, the team:
- decomposed the system using a causality graph, a standard approach in Modelon’s modeling philosophy.
- broke the problem into progressively complex subprocesses.
- validated performance at each stage to ensure traceability and insight.
This physics-informed structure proved critical, not just for model accuracy, but for interpretability and refinement. It also reinforces an important principle: successful machine learning in simulation depends on system understanding, not just pure data.
Evaluating Machine Learning Models for Time-Series Simulation
Three machine learning architectures were evaluated to represent different approaches to time-series modeling. These models all provided their respective strengths and weaknesses in a simulation environment.
- Timewise Multi-Layer Perceptron (MLP)
A fast, simple baseline that performed well for low-complexity tasks but struggled with nonlinear dynamics - Gated Recurrent Unit (GRU)
A recurrent model designed for time-series data that consistently delivered the best balance of accuracy and training efficiency - Neural Controlled Differential Equation (Neural CDE)
A continuous-time approach capable of modeling complex behavior, but difficult to implement and computationally expensive
Across all experiments, the GRU emerged as the most practical option, achieving strong accuracy without excessive training or computational effort.
Where Machine Learning Performs Well and Where It Doesn’t
One of the most important findings from the project is that machine learning performance is fundamentally tied to the information available.
When predicting vehicle speed from driver inputs and powertrain variables, a process without an explicitly defined physics model, the results were strong, with R² values around 0.98. This highlights the value of ML in situations where building a detailed physical model would be time-consuming or impractical.
However, predicting forces and torques using only driver inputs proved significantly more difficult. The models struggled because the available inputs did not fully capture the system’s underlying dynamics.
The breakthrough came when the models were given the same positional and dynamic inputs used by the physics-based simulation:
- The GRU model replicated forces and torques almost perfectly.
- R² values approached 0.99.
- Results closely matched the original Modelica simulation outputs.
This demonstrates critical insight for engineering teams. This shows that machine learning can match high‑fidelity physical models, provided it is given sufficient information to work with.
Speed vs. Fidelity: A Practical Engineering Tradeoff
For simulation engineers, the tradeoff between accuracy and speed is a daily reality. Physics-based Modelica simulations provide trusted, high-fidelity results, but for highly nonlinear systems they can take hours to compute. This is well suited for deep analysis but less practical for rapid iteration, real-time feedback, or large-scale design exploration.
Machine learning thus introduces a compelling alternative:
- Simulation results can be reproduced in seconds instead of hours.
- High levels of accuracy are achievable for many use cases.
- Iterative workflows become significantly faster and more scalable.
This enables new capabilities such as interactive design studies, real-time feedback loops, and large parameter sweeps that would otherwise be impractical.
The Path Forward: ML and Physics as Complementary Approaches
The most important takeaway is not machine learning versus physics-based simulation; it’s how the two work together. This thesis clearly demonstrates the power of both approaches:
- Physics-based models provide accuracy, validation, and physical insight.
- Machine learning models provide speed and computational efficiency.
In particular, using physics-based simulations to generate target variables then training ML models on those variables proved highly effective. This allows computationally expensive components to be replaced with fast, data-driven surrogates.
This approach aligns closely with Modelon’s broader vision: AI should enhance physics-based modeling, not replace it. As these workflows mature, they can be integrated into platforms like Modelon Impact and extended through FMI-based ecosystems to enable more interactive and scalable engineering processes.
Where Simulation Is Headed Next
This thesis reflects a broader shift already underway across engineering organizations. Simulation is no longer just about accuracy. It is about enabling faster decisions, broader exploration, and more responsive engineering workflows. The future lies in combining the strengths of both approaches:
- Physics-based modeling for trust, traceability, and deep insight
- Machine learning for speed, scalability, and adaptability
For engineering teams, the opportunity is clear: identify where computation is the bottleneck and apply machine learning strategically to remove it. In that balance, simulation evolves from the bottleneck, racing into a competitive advantage.
