arXiv subjects

Christian Weißenfels

Publications and source records attributed to Christian Weißenfels.

6 recordsLinked to original sources

arXiv2026

Guided Diffusion by Optimized Loss Functions on Relaxed Parameters for Inverse Material Design

Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate step, which is an optimization problem by itself. In many scenarios, several design parameters can lead to the same or similar output values. For such cases, multi-modal probabilistic approaches are advantageous to obtain diverse solutions. A major difficulty in inverse design stems from the structure of the design space, since discrete parameters or further constraints disallow the direct use of gradient-based optimization. To tackle this problem, we propose a novel inverse design method based on diffusion models. Our approach relaxes the original design space into a continuous grid representation, where gradients can be computed by implicit differentiation in the forward simulation. A diffusion model is trained on this relaxed parameter space in order to serve as a prior for plausible relaxed designs. Parameters are sampled by guided diffusion using gradients that are propagated from an objective function specified at inference time through the differentiable simulation. A design sample is obtained by backprojection into the original parameter space. We develop our approach for a composite material design problem where the forward process is modeled as a linear FEM problem. We evaluate the performance of our approach in finding designs that match a specified bulk modulus. We demonstrate that our method can propose multiple diverse designs within 1% relative error margin from medium to high target bulk moduli in 2D and 3D settings. We also demonstrate that the material density of generated samples can be minimized simultaneously by using a multi-objective loss function.

cs.LG↗

arXiv2026

Improved Training Strategies for Physics-Informed Neural Networks using Real Experimental Data in Aluminum Spot Welding

Resistance spot welding is the dominant joining process for the body-in-white in the automotive industry, where the weld nugget diameter is the key quality metric. Its measurement requires destructive testing, limiting the potential for efficient quality control. Physics-informed neural networks were investigated as a promising tool to reconstruct internal process states from experimental data, enabling model-based and non-invasive quality assessment in aluminum spot welding. A major challenge is the integration of real-world data into the network due to competing optimization objectives. To address this, we introduce two novel training strategies. First, experimental losses for dynamic displacement and nugget diameter are progressively included using a fading-in function to prevent excessive optimization conflicts. We also implement a custom learning rate scheduler and early stopping based on a rolling window to counteract premature reduction due to increased loss magnitudes. Second, we introduce a conditional update of temperature-dependent material parameters via a look-up table, activated only after a loss threshold is reached to ensure physically meaningful temperatures. An axially symmetric two-dimensional model was selected to represent the welding process accurately while maintaining computational efficiency. To reduce computational burden, the training strategies and model components were first systematically evaluated in one dimension, enabling controlled analysis of loss design and contact models. The two-dimensional network predicts dynamic displacement and nugget growth within the experimental confidence interval, supports transferring welding stages from steel to aluminum, and demonstrates strong potential for fast, model-based quality control in industrial applications.

cs.LG↗

arXiv2025

Robust and efficient pre-processing techniques for particle-based methods including dynamic boundary generation

Obtaining high-quality particle distributions for stable and accurate particle-based simulations poses significant challenges, especially for complex geometries. We introduce a preprocessing technique for 2D and 3D geometries, optimized for smoothed particle hydrodynamics (SPH) and other particle-based methods. Our pipeline begins with the generation of a resolution-adaptive point cloud near the geometry's surface employing a face-based neighborhood search. This point cloud forms the basis for a signed distance field, enabling efficient, localized computations near surface regions. To create an initial particle configuration, we apply a hierarchical winding number method for fast and accurate inside-outside segmentation. Particle positions are then relaxed using an SPH-inspired scheme, which also serves to pack boundary particles. This ensures full kernel support and promotes isotropic distributions while preserving the geometry interface. By leveraging the meshless nature of particle-based methods, our approach does not require connectivity information and is thus straightforward to integrate into existing particle-based frameworks. It is robust to imperfect input geometries and memory-efficient without compromising performance. Moreover, our experiments demonstrate that with increasingly higher resolution, the resulting particle distribution converges to the exact geometry.

math.NA↗

arXiv2022

Parallel Multiphysics Simulation for the Stabilized Optimal Transportation Meshfree (OTM)

This paper presents a parallel \PG{implementation} for the Optimal Transportation Meshfree (OTM) method on large CPU clusters. Communications are handled with the Message Passing Interface (MPI). The Recursive Coordinate Bisection (RCB) algorithm is utilized for domain decomposition and for implementing dynamic load-balancing strategy. This work involves three new concepts to reduce the computational efforts: Dynamic halo regions, Efficient data management strategies for ease of addition and deletion of nodes and material points using advanced STL container, and nearest neighborhood communication for detection of neighbors and communication. Also, Linked Cell approach has been implemented to further reduce the computational efforts. Parallel performance analysis is investigated for challenging multiphysics applications like Taylor rod impact and serrated chip formation process. Adequate scalability of parallel implementation for these applications is reported.

cs.CE↗

arXiv2020

The Neural Particle Method -- An Updated Lagrangian Physics Informed Neural Network for Computational Fluid Dynamics

Numerical simulation is indispensable in industrial design processes. It can replace expensive experiments and even reduce the need for prototypes. While products designed with the aid of numerical simulation undergo continuous improvement, this must also be true for numerical simulation itself. Up to date, no general purpose numerical method is available which can accurately resolve a variety of physics ranging from fluid to solid mechanics including large deformations and free surface flow phenomena. These complex multi-physics problems occur for example in Additive Manufacturing processes. In this sense, the recent developments in Machine Learning display promise for numerical simulation. It has recently been shown that instead of solving a system of equations as in standard numerical methods, a neural network can be trained solely based on initial and boundary conditions. Neural networks are smooth, differentiable functions that can be used as a global ansatz for Partial Differential Equations (PDEs). While this idea dates back to more than 20 years ago [Lagaris et al., 1998], it is only recently that an approach for the solution of time dependent problems has been developed [Raissi et al., 2019]. With the latter, implicit Runge Kutta schemes with unprecedented high order have been constructed to solve scalar-valued PDEs. We build on the aforementioned work in order to develop an Updated Lagrangian method for the solution of incompressible free surface flow subject to the inviscid Euler equations. The method is easy to implement and does not require any specific algorithmic treatment which is usually necessary to accurately resolve the incompressibility constraint. Due to its meshfree character, we will name it the Neural Particle Method (NPM). It will be demonstrated that the NPM remains stable and accurate even if the location of discretization points is highly irregular.

math.NA↗

arXiv2020

A machine learning based plasticity model using proper orthogonal decomposition

Data-driven material models have many advantages over classical numerical approaches, such as the direct utilization of experimental data and the possibility to improve performance of predictions when additional data is available. One approach to develop a data-driven material model is to use machine learning tools. These can be trained offline to fit an observed material behaviour and then be applied in online applications. However, learning and predicting history dependent material models, such as plasticity, is still challenging. In this work, a machine learning based material modelling framework is proposed for both elasticity and plasticity. The machine learning based hyperelasticity model is developed with the Feed forward Neural Network (FNN) directly whereas the machine learning based plasticity model is developed by using of a novel method called Proper Orthogonal Decomposition Feed forward Neural Network (PODFNN). In order to account for the loading history, the accumulated absolute strain is proposed to be the history variable of the plasticity model. Additionally, the strain-stress sequence data for plasticity is collected from different loading-unloading paths based on the concept of sequence for plasticity. By means of the POD, the multi-dimensional stress sequence is decoupled leading to independent one dimensional coefficient sequences. In this case, the neural network with multiple output is replaced by multiple independent neural networks each possessing a one-dimensional output, which leads to less training time and better training performance. To apply the machine learning based material model in finite element analysis, the tangent matrix is derived by the automatic symbolic differentiation tool AceGen. The effectiveness and generalization of the presented models are investigated by a series of numerical examples using both 2D and 3D finite element analysis.

cs.CE↗