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Towards a Digital Twin Framework in Additive Manufacturing: Machine Learning and Bayesian Optimization for Time Series Process Optimization
Vispi Karkaria, Anthony Goeckner, Rujing Zha, Jie Chen, Jianjing Zhang, Qi Zhu, Jian Cao, Robert X. Gao, Wei Chen
TL;DR
DED parts face heterogeneous properties and part-to-part variation, while optimizing laser-power time series can require costly iterations. This paper combines a Bayesian LSTM surrogate with reduced-dimensional Bayesian optimization in a digital-twin framework; the offline optimization maximized heat-treatment time to 38.19 seconds.
Problem
DED fabrication is associated with heterogeneous and anisotropic mechanical properties, part-to-part variation, and thermal accumulation, while detailed-physics optimization can be costly.
Source: §1 · pp. 1–2Method
The paper proposes a digital-twin framework using a Bayesian LSTM surrogate for temperature prediction and a low-dimensional representation of time-series laser-power inputs for Bayesian optimization.
Source: §1 · p. 2, §4 · p. 10Results
38.19 seconds: heat-treatment time was maximized to this value, and the Bayesian LSTM achieved an R4 score of 0.75 on a thin-wall geometry.
Source: §4 · pp. 10–11Takeaways & Limitations
The offline optimized process trajectory is intended to serve as the reference trajectory for online model predictive control.
Source: §4 · p. 11Integration with a physical DED system remains future work, including online laser-power optimization, continuous model updates, and surrogate-model drift correction.
Source: §4 · p. 11
Abstract
from arXiv · showhide
Laser-directed-energy deposition (DED) offers advantages in additive manufacturing (AM) for creating intricate geometries and material grading. Yet, challenges like material inconsistency and part variability remain, mainly due to its layer-wise fabrication. A key issue is heat accumulation during DED, which affects the material microstructure and properties. While closed-loop control methods for heat management are common in DED research, few integrate real-time monitoring, physics-based modeling, and control in a unified framework. Our work presents a digital twin (DT) framework for real-time predictive control of DED process parameters to meet specific design objectives. We develop a surrogate model using Long Short-Term Memory (LSTM)-based machine learning with Bayesian Inference to predict temperatures in DED parts. This model predicts future temperature states in real time. We also introduce Bayesian Optimization (BO) for Time Series Process Optimization (BOTSPO), based on traditional BO but featuring a unique time series process profile generator with reduced dimensions. BOTSPO dynamically optimizes processes, identifying optimal laser power profiles to attain desired mechanical properties. The established process trajectory guides online optimizations, aiming to enhance performance. This paper outlines the digital twin framework's components, promoting its integration into a comprehensive system for AM.
1. Introduction
DED’s layer-wise thermal history contributes to variable material properties, while existing control and modeling approaches leave gaps in online, uncertainty-aware optimization. The paper proposes a digital-twin approach combining Bayesian temperature prediction with low-dimensional time-series optimization.
1. Introduction
- DED parts exhibit heterogeneous and anisotropic mechanical properties and part-to-part variation, limiting application.DED also offers near-net-shape fabrication of freeform geometries with internal features and material grading.Source: §1 · p. 1
- DED’s layer-wise thermal cycles create uneven histories; heat accumulation can alter chemistry, while heterogeneous cooling can produce spatially varying mechanical properties.The cited discussion also notes that secondary energy sources for microstructure control increase cost and complexity.Source: §1 · pp. 1–2
- Prior DED controllers regulate melt-pool temperature, but feedback-only schemes do not use known-a-priori disturbances, and adding physics can increase cycle time.The cited work describes a hybrid feedback-feedforward system that maintained melt-pool temperatures by adjusting laser power.Source: §1 · p. 2
- A DED digital twin should estimate unobserved targets, update online, and communicate state changes for control; many existing systems lack online-control-ready computation and bidirectional exchange.The paper characterizes such systems as “digital shadows.”Source: §1 · p. 2
- Prior temperature models leave gaps in dynamic laser-power testing, uncertainty quantification, or real-time prediction needed for online decision-making.The heat-conduction graph network accommodates variable laser power, but the cited work lacks uncertainty quantification and real-time prediction.Source: §1 · p. 2
- Offline laser-profile optimization can be expensive because accurate DED simulations require detailed physics, while differentiable-surrogate approaches can have high memory requirements.The paper identifies minimizing optimization iterations as beneficial.Source: §1 · p. 2
- The paper proposes a DED digital twin with Bayesian LSTM temperature prediction and low-dimensional Bayesian optimization of laser-power profiles.The optimization targets maximizing heat-treatment time throughout DED-built parts.Source: §1 · p. 2
2. Digital Twin (DT) framework for the Additive Manufacturing Process
The proposed DED digital twin links a physical process with a digital system for bidirectional information exchange and online control. Its digital side uses an updated surrogate model and offline optimization to support model predictive control.
2. Digital Twin (DT) framework for the Additive Manufacturing Process
- The framework combines physics-based models, real-time data collection, and model predictive control, with continuous online data used to maintain model accuracy.The paper contrasts this bidirectional approach with digital shadows and one-time offline validation.Source: §2 · p. 3
- The physical manufacturing process and digital system are linked through bidirectional information exchange; process parameters such as laser power are controlled and monitored by sensors.The digital system is shown as the right-hand block and the physical process as the left-hand block.Source: §2 · p. 3
- A surrogate time-series model replaces expensive FEM simulations for real-time analysis, with data from both systems used to update predictions under aleatoric and epistemic uncertainty.The offline-updated surrogate feeds online MPC, which optimizes actions over a finite horizon using the current state, predictive model, and objective.Source: §2 · p. 3
- This work focuses on developing the surrogate model and offline process optimization within the digital system.Source: §2 · p. 3
3. The Bayesian LSTM network as a surrogate model
The Bayesian LSTM surrogate predicts temperatures at selected DED locations from spatial, deposition, laser-power, and prior-temperature information. It is trained on FEM-generated histories and evaluated for surface and internal temperature prediction.
3.1 Architecture of the Bayesian LSTM model
- Each node’s current temperature is predicted from spatial and deposition context, current laser power, and prior temperature, with time-invariant and time-varying inputs handled in separate paths.The time-invariant path feeds a 100-node forward layer corresponding to spatial information.Source: §3.1 · p. 4, Figure 2
- Attention weights emphasize selected time steps, while Monte Carlo dropout samples predictions whose variance quantifies uncertainty and also regularizes the model.The model uses two LSTM layers with 500 units and a 100-node feedforward layer to aggregate temporal and spatial features.Source: §3.1 · pp. 4–5
3.2 Bayesian LSTM model training strategy
- GPU-accelerated FEM simulations supplied temperature histories, sampled every 0.02 seconds, across laser profiles for training.The simulation used an explicit 0.002-second time step, with data gathered every 10 steps.Source: §3.2 · pp. 5–6
- Laser-profile training simulations varied frequency, mean, and variance using Latin Hypercube sampling, then generated and filtered profiles through MCMC.The training strategy used 50 parameter sets with specified bounds for mean, variance, and frequency.Source: §3.2 · pp. 5–6
- Randomly sampled, overlapping windows from 80 profiles and all 96,000 FEM nodes support location-agnostic training; each window contains time-series data.The latter half of each window also serves as the former half of the next window.Source: Figure 5 · p. 5, §3.2 · p. 6
- Training uses an evidence lower bound loss balancing expected log-likelihood against KL-divergence regularization.The authors report that experimentation found ELBO effective for training the surrogate model.Source: §3.2 · p. 6
3.3 Evaluation of the LSTM Model
- 0.75 𝑅4 score was reported; Fig. 6 shows close prediction–ground-truth alignment, with poorer, high-biased predictions when the laser is farther from a node.The figure compares three locations over 280 seconds with a 95% uncertainty band.Source: §3.3 · p. 6, Figure 6 · p. 6
- The model reliably predicts internal temperatures for six seconds at 95% confidence, but recursive errors accumulate substantially past the first temperature peak.For internal forecasts, prior model predictions can be used as inputs when temperatures are unobservable.Source: §3.3 · pp. 6–7
4. Bayesian Optimization for Time Series Process Optimization (BOTSPO)
BOTSPO combines a compact time-series laser-power profile with Gaussian-process Bayesian optimization to search for DED process settings that maximize heat-treatment time. In the reported optimization, the profile favored high initial power, but maximizing duration alone did not produce material homogeneity.
4. Bayesian Optimization for Time Series Process Optimization (BOTSPO)
- BOTSPO represents laser power with a Fourier-based profile whose changing amplitude, frequency, and phase, plus trend and seasonality terms, capture profile evolution over time.The authors report ten tunable parameters, selected to balance profile representation and computational efficiency.Source: §4.1 · pp. 7–8
- A Gaussian-process model maps the profile parameters to the objective, while an upper-confidence-bound acquisition rule selects profiles and adaptively balances exploration with exploitation.The exploration parameter responds to recent prediction uncertainty as the search proceeds.Source: §4.1 · pp. 8–9
4.2 Results from the BOTSPO method
- The objective maximizes the sampled duration that temperatures across build nodes remain within a desired range, motivated here by IN718’s in-situ aging objective.The paper relates local IN718 strength to time spent between 654°C and 857 °C.Source: §4.2 · p. 9
- BOTSPO’s function-call history moved from early exploration toward later plateaus, and the authors report sample-efficient optimization with fewer data points and reduced computational expense.The GP model was pretrained on 50 laser-power profile samples before integration into BOTSPO.Source: §4.2 · p. 9, Figure 10 · p. 10
- The optimized profile used high initial laser power, then avoided increasing power later because greater power did not substantially improve total heat-treatment duration.As the thin wall grew, radiative and convective heat transfer increased and heat-treatment time decreased at higher locations.Source: Figure 9 · p. 9, §4.2 · p. 10
- The duration-focused result increased average heat-treatment time but did not achieve material homogeneity, motivating future multi-objective optimization.The proposed future objective would balance heat-treatment duration and homogeneity to prevent the front-biased result.Source: §4.2 · p. 10
- The resulting offline laser-power profile provides a process trajectory intended to guide online predictive control during DED.Source: §4.2 · p. 10
4. Conclusion
The conclusion presents an autonomous DED digital twin combining real-time, uncertainty-aware temperature prediction with BOTSPO laser-profile optimization. On a thin-wall IN718 build, BOTSPO maximized heat-treatment time at 38.19 seconds; physical-system integration remains future work.
4. Conclusion
- The proposed DED digital twin combines real-time temperature prediction and laser-power-profile optimization for repeatable fabrication of complex parts.The framework's two components are a temperature surrogate with uncertainty quantification and BOTSPO, which identifies laser-power profiles.Source: §4 · p. 10
- The Bayesian LSTM predicts temperatures in real time and quantifies uncertainty, with an R^2 score of 0.75 on a thin-wall geometry.The model is laser-profile agnostic and predicts temperatures at selected areas of the built part.Source: §4 · p. 10
- 38.19 seconds was the maximum heat-treatment time for the thin-wall IN718 build using BOTSPO.The offline optimization result serves as the reference process trajectory for online model predictive control.Source: §4 · pp. 10–11
- Integration with a physical DED system remains future work, including online laser-power optimization, continuous model updates, and surrogate-model drift correction.The proposed framework components have not yet been integrated with a physical DED system.Source: §4 · p. 11