Hybrid full-field thermal characterization of additive manufacturing processes using physics-informed neural networks with data

Understanding the thermal behavior of additive manufacturing (AM) processes is crucial for enhancing the quality control and enabling customized process design. Most purely physics-based computational models suffer from intensive computational costs, thus not suitable for online control and iterative design application. Data-driven models taking advantage of the latest developed computational tools can serve as a more efficient surrogate, but they are usually trained over a large amount of simulation data and often fail to effectively use small but high-quality experimental data. In this work, we developed a hybrid physics-based data-driven thermal modeling approach of AM processes using physics-informed neural networks. Specifically, partially observed temperature data measured from an infrared camera is combined with the physics laws to predict full-field temperature history and to discover unknown material and process parameters. In the numerical and experimental examples, the effectiveness of adding auxiliary training data and using the technique of transfer learning on training efficiency and prediction accuracy, as well as the ability to identify unknown parameters with partially observed data, are demonstrated. The results show that the hybrid thermal model can effectively identify unknown parameters and capture the full-field temperature accurately, and thus it has the potential to be used in iterative process design and real-time process control of AM.

Learning the nonlinear dynamics of soft mechanical metamaterials with graph networks

The dynamics of soft mechanical metamaterials provides opportunities for many exciting engineering applications. Previous studies often use discrete systems, composed of rigid elements and nonlinear springs, to model the nonlinear dynamic responses of the continuum metamaterials. Yet it remains a challenge to accurately construct such systems based on the geometry of the building blocks of the metamaterial. In this work, we propose a machine learning approach to address this challenge. A metamaterial graph network (MGN) is used to represent the discrete system, where the nodal features contain the positions and orientations the rigid elements, and the edge update functions describe the mechanics of the nonlinear springs. We use Gaussian process regression as the surrogate model to characterize the elastic energy of the nonlinear springs as a function of the relative positions and orientations of the connected rigid elements. The optimal model can be obtained by "learning" from the data generated via finite element calculation over the corresponding building block of the continuum metamaterial. Then, we deploy the optimal model to the network so that the dynamics of the metamaterial at the structural scale can be studied. We verify the accuracy of our machine learning approach against several representative numerical examples. In these examples, the proposed approach can significantly reduce the computational cost when compared to direct numerical simulation while reaching comparable accuracy. Moreover, defects and spatial inhomogeneities can be easily incorporated into our approach, which can be useful for the rational design of soft mechanical metamaterials.

Amortized Synthesis of Constrained Configurations Using a Differentiable Surrogate

In design, fabrication, and control problems, we are often faced with the task of synthesis, in which we must generate an object or configuration that satisfies a set of constraints while maximizing one or more objective functions. The synthesis problem is typically characterized by a physical process in which many different realizations may achieve the goal. This many-to-one map presents challenges to the supervised learning of feed-forward synthesis, as the set of viable designs may have a complex structure. In addition, the non-differentiable nature of many physical simulations prevents direct optimization. We address both of these problems with a two-stage neural network architecture that we may consider to be an autoencoder. We first learn the decoder: a differentiable surrogate that approximates the many-to-one physical realization process. We then learn the encoder, which maps from goal to design, while using the fixed decoder to evaluate the quality of the realization. We evaluate the approach on two case studies: extruder path planning in additive manufacturing and constrained soft robot inverse kinematics. We compare our approach to direct optimization of design using the learned surrogate, and to supervised learning of the synthesis problem. We find that our approach produces higher quality solutions than supervised learning, while being competitive in quality with direct optimization, at a greatly reduced computational cost.

Learning Composable Energy Surrogates for PDE Order Reduction

Meta-materials are an important emerging class of engineered materials in which complex macroscopic behaviour--whether electromagnetic, thermal, or mechanical--arises from modular substructure. Simulation and optimization of these materials are computationally challenging, as rich substructures necessitate high-fidelity finite element meshes to solve the governing PDEs. To address this, we leverage parametric modular structure to learn component-level surrogates, enabling cheaper high-fidelity simulation. We use a neural network to model the stored potential energy in a component given boundary conditions. This yields a structured prediction task: macroscopic behavior is determined by the minimizer of the system's total potential energy, which can be approximated by composing these surrogate models. Composable energy surrogates thus permit simulation in the reduced basis of component boundaries. Costly ground-truth simulation of the full structure is avoided, as training data are generated by performing finite element analysis with individual components. Using dataset aggregation to choose training boundary conditions allows us to learn energy surrogates which produce accurate macroscopic behavior when composed, accelerating simulation of parametric meta-materials.