Bridging the Gap: How Inverse Problem Solving Transforms Functional Requirements into Technical Specifications

Apr 29
4 min read

From "What If?" to "What's Needed?" – A New Approach to Engineering Design

As simulation engineers, we solve typical “forward problems” often. We’re given the geometry, the material properties, and the key boundary conditions, and are asked what might happen. Given that a structural part has this radius and that thickness, what static load can it withstand before failure? State the assumptions, build and validate the model against literature/experimental data and common pitfalls, and provide the results. But what if we could flip the script? What if, instead of asking "what will happen with these properties?", we could answer "what properties do we need to achieve these results?" This is the power of solving inverse problems, and it's transforming how our clients approach technology development and system design.

A Real-World Challenge: Gas Separation Technology

Let's explore this concept through a recent project we presented at the 2024 COMSOL Conference Boston. We worked with a team developing spiral-wound membrane systems for separating and enriching gas flows [1]. The candidate system’s performance could be estimated with a few key input parameters (e.g., membrane and flow properties) and output performance metrics. After refinement and validation of the computational model against empirical data and analytical models, it was possible to run broad parametric sweeps to show expected performance against a variety of combinations of input properties. That’s the forward problem: given input parameters, what is the system output/performance?

However, the purpose of this simulation effort was to bridge the gap between technology development (polymer membrane synthesis) and system design (the gas separation application). The system designer had requirements for the performance of the applied technology, which lead to decisions on system sizing and component selection. Demonstrating that these targets are feasible with a certain set of membrane properties is valuable to know early in the design process. The system designer might also need to know some key tradeoffs given the state of the underlying technology.

Two teams were working in parallel but speaking different languages:

The membrane development team was synthesizing new polymer materials with specific permeability and selectivity properties
The system design team needed modules that met functional requirements: specific enrichment factors and permeation rates to determine system sizing and component selection

The membrane developers were essentially playing a guessing game: create a material, test its properties, send it to the system designers, and see if it meets their needs. This iterative approach was time-consuming and inefficient. What the membrane development team really needed were specific development targets that would guarantee their materials would work in the final application. This is where inverse problem solving comes in. Instead of asking "given these membrane properties, what performance will we get?", we asked: "Given the performance requirements, what membrane properties will deliver those results?"

The Solution: Deep Neural Networks and Surrogate Modeling

To solve the inverse problem efficiently, we can turn to Deep Neural Networks (DNN) and machine learning to build numerical predictors from our simulation results. COMSOL’s Surrogate Modeling feature (introduced in Version 6.2) helped to bring this capability into a single cohesive environment. Training data is generated by automatically running the full FEA model many times over distributed/sampled ranges of input parameters. Forward and inverse DNN predictors are trained and validated using the input/output parameter tables. Validation of the forward predictors is significantly easier to accomplish with test cases, and the validated forward DNNs allow for the use of synthetic data to more rapidly train and validate the inverse DNNs. From there, design curves/surfaces can be generated from the trained DNN functions which help to define the complete problem space.

Visualizing the Design Space

The power of this approach becomes clear when we visualize the results. For example, here are some arbitrary design curves for a well-behaved system with two input parameters (x₁, x₂) and two output parameters (y₁, y₂), where we are plotting on axes of one output y₁ versus one input x₁. The solid lines are generated from the forward problem, representing isocurves of x₂ (e.g., the green line plots y₁ vs. x₁ given that x₂=2). The dotted lines come from the inverse problem and are isocurves of output y₂. Intersections between these curves represent complete solutions to the problem – the intersection of the blue line (x₂=1) and black dotted line (y₂=8) looks to be at about x₁=0.5 and y₁=3.5, so we can deduce that (x₁=0.5, x₂=1, y₁=3.5, y₂=8) is a valid solution.

The Impact: From Guesswork to Guided Development

This inverse problem approach delivered several key benefits:

Targeted Development: The membrane team now had specific property targets to guide their synthesis work
Reduced Iteration: No more guess-and-check cycles between development and system design teams
Complete Design Space Understanding: Both teams could see the full range of feasible solutions and understand key tradeoffs
Faster Time to Market: Eliminating unnecessary development cycles accelerated the overall project timeline

When Should You Consider Inverse Problem Solving?

Inverse problem solving isn't always necessary or even feasible for every project. But it's particularly powerful when:

Multiple teams are working on different aspects of a system with interdependent requirements
Functional specifications need to be translated into technical property targets
The design space is complex with multiple input-output relationships
Development cycles are expensive or time-consuming
You need to understand the complete feasible design space, not just point solutions

Your Challenges, Our Capabilities

At TRACE Simulation, we specialize in bringing advanced simulation techniques to practical engineering challenges. Whether you're developing new materials, designing complex systems, or trying to bridge the gap between functional requirements and technical specifications, we can help you leverage the power of computational modeling.

Ready to explore how simulation can accelerate your development process?

Learn more about this project in our COMSOL Conference poster: Selectively Permeable Membrane Gas Separation System Modeling and DNN Tool Development [1]