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arxiv: 2604.16649 · v1 · submitted 2026-04-17 · 💻 cs.LG

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FLARE: A Data-Efficient Surrogate for Predicting Displacement Fields in Directed Energy Deposition

Kittipong Thiamchaiboonthawee , Ghadi Nehme , Ram Mohan Telikicherla , Jiawei Tian , Balaji Jayaraman , Vikas Chandan , Dhanushkodi Mariappan , Faez Ahmed
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keywords affinedisplacementdata-efficientdepositionfieldsflareframeworkprediction
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The pith

FLARE predicts post-cooling displacement fields in directed energy deposition by encoding simulations as implicit neural fields whose weights are regularized to follow an affine structure in parameter space, enabling data-efficient prediction via weight mixing.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Directed energy deposition builds metal parts by melting powder with a laser. The heat creates stresses that distort the finished part, so engineers run detailed computer simulations to predict the final shape. These simulations are accurate but take too long to run for every possible design, laser power, and speed. FLARE creates a fast stand-in model. It first runs a set of simulations for different shapes and settings. Each full simulation result is stored inside a small neural network that can output the displacement at any point in the part. The key step is to adjust the training of these networks so their internal numbers (the weights) change in a straight-line, or affine, way when the input parameters change. To predict a new combination of shape, power, and speed, FLARE simply blends the weights from the training networks using the same straight-line rule. Tests on the generated DED examples showed this blending produced more accurate displacement maps than standard machine-learning baselines, both for cases close to the training data and for cases outside it. The approach needs fewer simulations than training a new model from scratch for every query.

Core claim

On this DED benchmark, the method shows improved accuracy compared to baseline methods in both in-distribution and extrapolation settings.

Load-bearing premise

The neural-network weights that encode each simulation's displacement field lie on an affine subspace in weight space that is aligned with the input parameter space, so that unseen parameter combinations can be reconstructed by linear mixing of training weights.

Figures

Figures reproduced from arXiv: 2604.16649 by Balaji Jayaraman, Dhanushkodi Mariappan, Faez Ahmed, Ghadi Nehme, Jiawei Tian, Kittipong Thiamchaiboonthawee, Ram Mohan Telikicherla, Vikas Chandan.

Figure 1
Figure 1. Figure 1: FIGURE 1: DED Modeling Schematic [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIGURE 2: Geometry, Mesh, and Printing Path [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIGURE 4: Overview of the FLARE method. Each physical field is represented by an implicit neural network. A linear relationship between [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIGURE 5: Radial hull-distance visualization of the parameter [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIGURE 6: Sample Ground Truth, Prediction, and Error [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIGURE 7: Metric vs Size of Training Set [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
read the original abstract

Directed energy deposition (DED) produces complex thermo-mechanical responses that can lead to distortion and reduced dimensional accuracy of a manufactured part. Thermo-mechanical finite element simulations are widely used to estimate these effects, but their computational cost and the complexity of accurately capturing DED physics limit their use in design iteration and process optimization. This paper introduces FLARE (Field Prediction via Linear Affine Reconstruction in wEight-space), a data-efficient surrogate modeling framework for predicting post-cooling displacement fields in DED from geometric and process parameters. We develop a predefined-geometry DED simulation workflow using an open-source finite element framework and generate a dataset of simulations with varying geometry, laser power, and deposition velocity. Each simulation provides full-field displacement, stress, strain, and temperature data throughout the manufacturing process. FLARE encodes each simulation as an implicit neural field and regularizes the corresponding neural-network weights so that they follow the affine structure of the input parameter space. This enables prediction of unseen parameter combinations by reconstructing network weights through affine mixing of training examples. On this DED benchmark, the method shows improved accuracy compared to baseline methods in both in-distribution and extrapolation settings. Although the present study focuses on DED displacement prediction, the proposed affine weight-space reconstruction framework offers a promising approach for data-efficient surrogate modeling of physical fields.

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Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on two domain assumptions: that implicit neural fields can faithfully represent full-field DED simulation outputs, and that the resulting network weights admit an affine parameterization with respect to the input geometry and process variables. No free parameters or invented physical entities are introduced in the abstract.

axioms (2)
  • domain assumption Displacement, stress, strain, and temperature fields from DED simulations can be accurately encoded by implicit neural fields.
    The method presupposes that a neural network can serve as a lossless or near-lossless representation of the simulation output fields.
  • ad hoc to paper The weights of these neural fields vary affinely with the input geometric and process parameters.
    This is the key modeling choice that enables weight-space mixing for unseen parameter combinations.

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