A research team from Nanjing Tech University, a Chinese institution specializing in mechanical and power engineering research, has introduced a physics-informed neural operator (PINO) framework capable of predicting real-time distortion in Wire Arc Additive Manufacturing (WAAM)—also known as Directed Energy Deposition-Arc (DED-Arc). Published on arXiv, the study presents PIDeepONet-RNN, a model that forecasts thermo-mechanical distortion up to 15 seconds ahead in both z- and y-directions. It achieved maximum absolute errors of 0.9733 mm and 0.2049 mm, respectively, while performing predictions in under 150 milliseconds—a significant reduction from the four hours required by traditional finite-element simulations.
Finite Element Method (FEM) and Computational Fluid Dynamics (CFD) simulations capture detailed thermo-mechanical responses in WAAM but demand extensive computational time. FEM typically requires several hours to simulate a few seconds of deposition, while CFD can take weeks. These models must also be recalibrated whenever process parameters or geometries change. Machine-learning surrogates such as convolutional neural networks (CNNs) or spatiotemporal ConvLSTM architectures have improved prediction speed, yet they struggle with long-horizon accuracy and cannot fully decouple the intertwined thermal and mechanical fields that drive distortion.
Nanjing Tech’s team addressed these limitations by combining operator learning with physical constraints derived from the heat-conduction equation. The PIDeepONet-RNN framework consists of a trunk network that learns the temporal evolution of temperature and a branch network that encodes mechanical response. Embedding the governing equation directly into the model’s loss function enforces physical consistency, constraining predictions to thermodynamically valid relationships. This integration allows accurate, long-horizon forecasting across varying deposition conditions without retraining.
Dataset generation and model structure
Researchers constructed an experimentally validated FEM dataset using ER70S-6 and Q235b low-carbon steels. The simulated geometry comprised a 300 × 300 × 10 mm substrate and a 100 mm-tall thin wall, meshed with hexahedral elements and heated by a Goldak double-ellipsoidal source. A zigzag scanning path and 60-second interlayer cooling time were applied to mitigate uneven heat buildup. Temperature and distortion data were sampled every second and normalized between 0 and 1, resulting in 6,880 training and 1,300 testing samples that captured diverse combinations of wire-feed and travel speeds.
Model training was executed on a single NVIDIA GeForce RTX 4050 GPU (6 GB) using PyTorch. Both branch and trunk networks employed convolutional and ConvLSTM layers connected by a Hadamard product to simulate coupled thermo-mechanical behavior. The total loss combined three components—data accuracy, trunk-temperature fidelity, and a physical residual term weighted by coefficients α, β, and λ—to maintain numerical precision and physical validity. Training spanned 5,000 epochs, reaching convergence after roughly 104 minutes, slightly longer than CNN and ConvLSTM baselines but yielding smoother stability and lower cumulative error. Once trained, the model generated full-field predictions within 150 milliseconds, compared with four hours for FEM computations.
Comparative results and quantitative evaluation
Four surrogate models—CNN, spatiotemporal ConvLSTM, DeepONet-RNN, and PIDeepONet-RNN—were benchmarked using Mean Absolute Error (MAE), Kullback–Leibler (KL) divergence, and Structural Similarity Index (SSIM). PIDeepONet-RNN recorded the lowest MAEs of 0.0261 mm (z-axis) and 0.0165 mm (y-axis) during the first five-second window, maintaining stability over a 15-second horizon. Gradient-norm analysis confirmed minimal error concentration in molten-pool and deposited regions, demonstrating effective learning of coupled thermal–mechanical evolution.
CNN performance degraded rapidly, with z-axis errors exceeding 1.2 mm, while ConvLSTM and DeepONet-RNN improved accuracy but suffered from temporal drift. Incorporating the heat-conduction constraint reduced the maximum absolute error by approximately 20 % relative to unconstrained models and prevented error accumulation during interlayer transitions where heat input and boundary conditions shift sharply.
Predicted von Mises stress distributions closely matched FEM benchmarks, with an average error of 2.3 % and maximum regional deviation of 9 %, confirming that physics-based regularization enhances realism without compromising computational efficiency.
Toward real-time digital twins in metallic AM
PIDeepONet-RNN demonstrates potential as a real-time distortion-prediction surrogate within WAAM control systems. Its architecture can directly integrate with in-situ sensors—including thermal cameras and laser scanners—to provide continuous feedback during layer-by-layer deposition. Unlike FEM, which must be rebuilt for each process change, the trained network generalizes to unseen parameters while maintaining predictive fidelity.
Embedding the heat-conduction equation enhances interpretability, allowing engineers to trace predicted distortion to underlying thermal history and stress evolution. This converts the model from a black-box predictor into a physically transparent diagnostic tool. Real-time inference capability positions the framework for digital-twin integration, enabling predictive monitoring, adaptive control, and defect mitigation in metallic additive manufacturing.
Future work will extend the approach to complex 3D geometries and incorporate deeper thermo-mechanical coupling laws. The research team also plans in-situ validation to bridge the simulation-to-reality gap and further refine predictive reliability for industrial adoption.
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Featured image shows Evaluation of surrogate models for z-direction distortion prediction for the future 1-15 s. Image via arXiv.
