Physics-informed Neural Network
Assembly Line
On machine learning methods for physics
Simulation methods are employed to resolve the behaviour of matter (solids, fluids, gases, etc.), fields (electromagnetic, pressure, velocity, density), and any number of other physical phenomena that are driven by known local rules, particularly partial differential equations (PDEs). Therefore, traditional simulation methods typically involve some kind of discretisation of the physical domain of interest, such that the rules of the governing PDE can be locally well-approximated by a tractable computation. Local computations are stacked together and iterated upon until we converge to a solution. Beyond a narrow class of problems where a closed-form solution can be provided, this is generally how complicated problems are addressed. Many PDEs can exhibit chaotic behaviour in their full form, which often causes us to resort to simpler approximations at the PDE level, even before discretisation, to make them computationally feasible and ensure convergence.
ML methods in general provide a new approach to accomplishing engineering tasks. Any of these methods greatly accelerate iterations in the design optimisation workflow, as they allow us to search the space faster and guide our search towards promising areas. This results in better exploration, overall lower computational costs for simulating physics, and ultimately, higher quality designs in a shorter time-frame and with lower manual effort.
The models discussed so far do not leverage the fact that we often know the PDE that generates data and governs solutions; the focus has been to approximate the physical laws from observations, rather than impose them in the model structure explicitly. This is primarily because of the difficulty of incorporating such prior knowledge into the models, but also because simulation data may disobey the exact PDE due to the approximations required to facilitate numerical simulations. However, a new approach to simulation has recently been proposed that takes advantage of this prior knowledge in an effort to reduce data requirements and promote physically consistent solutions. Physics-Informed Neural Networks (PINNs), as presented by Raissi, Perdikaris, and Karniadakis (2017a, 2017b; Zhu et al. 2019; Karniadakis et al. 2021) introduces an artificial neural network (ANN) that takes as input the coordinates of any point in the domain of the PDE, and outputs the value for the solution field at that point. The ANN is tasked with representing the solution field, and is trained by sampling points randomly in the domain and penalising deviations from the PDE at those points. As long as the activation function of the ANN is sufficiently differentiable, residuals in the terms of the PDE can be easily evaluated, which can be combined into the loss function to be minimised with respect to the ANN parameters. The ANN is an ansatz about a parametrised form of the solution (albeit a particularly flexible one) and we attempt to fit the parameters such that it best matches the PDE. The idea harks back to older variational numerical simulation methods, like the generalised Galerkin approximation and others.
Physics-Aware AI Is The Key To Next Gen IC Design
AI on the inside is a fundamentally different approach favored by Ansys where the core simulation and analysis algorithms are modified to operate with new AI understanding and new AI guidance. This serves to make the core engines run faster and give better results in terms of speed, capacity, and accuracy-vs-time efficiency. AI-inside achieves these benefits for all users and without any changes to the use model for the customer. A good example of AI-inside is the thermal simulation engine in RedHawk-SC Electrothermal for 3DIC analysis. Thermal simulation requires the creation of a finite element mesh as a first step. The finer the mesh the more accurate the result, but the simulation also takes longer. Ansys’ thermal engine is able to build an adaptive mesh that is fine only where it needs to be, around thermal hotspots, and is coarser elsewhere where a fine mesh is unnecessary. The problem with this approach is how to know ahead of time where these hotspots are located? AI offers a perfect solution for this because it can very quickly estimate a rough temperature distribution that is good enough to guide the adaptive mesh builder. The benefit is that it makes thermal simulation much faster without sacrificing any appreciable accuracy. This sort of enhancement under-the-hood is sometimes called bottom-up AI and it improves the fundamental operation of the tool any time thermal simulation is done in whatever context.
Advancements in Predicting the Fatigue Lifetime of Structural Adhesive Joints
While physics-based models offer the highest accuracy for analyzing these joints, they require meticulous parameter calibration for every new adhesive. For example, consider a fatigue test on a structural adhesive joint with 10 million cycles at a frequency of 10 Hz. These tests are demanding and time-consuming, taking over 10 days to complete. Adding to the challenge is the need for numerous data points to construct a comprehensive fatigue design curve, a fundamental aspect of structural analysis. Given the need to optimize both efficiency and accuracy, engineers and researchers need and pursue innovative solutions.
One path to solution is the integration of Artificial Intelligence (AI) and Machine Learning (ML) into materials science. Recognized for its ability to address complex problems through learning from existing knowledge, AI provides a promising avenue for structural modeling by generating mathematical expressions that capture the interplay of various parameters. We expect that this rationale also applies to the structural modelling of the fatigue behavior of structural adhesive joints, which is the subject of our ongoing research.
This showcase exemplifies our commitment to revolutionizing materials selection and fatigue life prediction for adhesive joints. Leveraging the Citrine Platform [2], we seamlessly apply machine learning methods to integrate experimental datasets with physics-based modeling (based on stress concentration factors). This innovative approach not only significantly elevates the precision of fatigue predictions but also enables the precise selection of optimal adhesives for bonded structures, factoring in various material and geometrical properties, as well as usage conditions.