AI-Driven Neural Operators for Modeling of Phase Transformations in Materials

SI2M (Science and Engineering of Materials and Metallurgy)

Organisation/Company Institut Jean Lamour

Department SI2M (Science and Engineering of Materials and Metallurgy)

Research Field Engineering » Materials engineering

Mathematics » Applied mathematics

Physics » Computational physics

Researcher Profile First Stage Researcher (R1)

Positions PhD Positions

Country France

Application Deadline 20 Apr 2025 - 23:59 (Europe/Paris)

Type of Contract Temporary

Job Status Full-time

Hours Per Week 35

Is the job funded through the EU Research Framework Programme? Not funded by a EU programme

Is the Job related to staff position within a Research Infrastructure? No

Offer Description

Background

Phase transformations play an important role in elaboration of metal materials because they determine the structure and, consequently, the properties of the material. They occur, for example, during the additive manufacturing (3D printing) of a metal part. First, the molten liquid metal transforms to a crystalline solid structure and then further phase transformations occur in solid state. The properties of the part depend on the final phases, their size and shape.

Phase-field models that describe these phase transformations are formulated by reaction-diffusion partial differential equations (PDEs). This description is such that it couples the phase transformations to external fields (temperature, chemical composition, stresses, liquid flow, etc.). Today, such PDEs are generally solved numerically with classical discretization methods (finite difference, finite element, Fourier spectral, etc.). The multi-scale and nonlinear nature of phase transformation models, however, requires fine space and time discretizations, leading to long computation times and costly simulations.

Recently developed artificial intelligence methods for approximating solutions of PDEs have the potential to be much faster and thus to revolutionize the modeling of phase transformations. These methods employ surrogate models based on neural networks (NN). Most NN training processes in literature are data-driven, requiring substantial datasets and suffering from limited generalization – ability to predict results that are outside the parameter range of the training set.

Better generalization is provided by Physics Informed Neural Network (PINN) type approaches. PINNs are trained to satisfy the governing physical equations by minimizing the residuals of the PDEs. A particularly practical approach of this type, that avoids some of the pitfalls of plain vanilla PINNs, are neural operators that learn the numerical scheme directly. Phase-field models offer another advantage: they can be formulated as a variational problem and can be solved by minimizing an energy functional rather than directly solving the PDEs. This strategy, leveraged by the Deep Ritz deep learning method, has been shown to be more efficient for highly nonlinear PDEs.

We recently developed a novel Reaction-Diffusion neural operator architecture for phase-field equations employing the Deep Ritz approach. We have shown that this architecture outperforms standard NN models for certain phase-field models (Allen-Cahn, dendritic solidification).

Objectives

The objectives of the PhD thesis are to extend the developed approaches to:

• achieve better accuracy of the PDE solution approximations with a suitable or more sophisticated neural network architecture;
• achieve better generality of the NN models in order to obtain robust out-of-distribution predictions;
• extend the Deep Ritz NN approaches to further phase-field models including other multiphysics couplings;
• develop NN approaches for sharp-interface formulations of phase transformations, such as the Stefan problem;
• develop similar NN approaches for phenomenological phase transformation models that can simulate larger spatial and temporal scales (such as the Grain Envelope Model for dendritic solidification).

This PhD offer is a collaborative project of IJL and IECL and is provided by the ENACT AI Cluster and its partners. Find all ENACT PhD offers and actions on https://cluster-ia-enact.ai.

Institut Jean Lamour (IJL) is one of the largest materials science research centers in Europe. The Department of Science and Engineering of Materials and Metallurgy (SI2M) focuses on processes ranging from liquid metal treatment over solidification to solid transformation processes; all with the objective to control the formation of the structure of the final product. We work in tight collaboration with the industry and with international academic partners on a wide spectrum of projects, integrating industrial and fundamental problems.

Specializing in a wide range of pure and applied mathematical disciplines, the Institut Élie Cartan de Lorraine (IECL) is one of France's largest mathematics laboratories. It has hosted world-renowned mathematicians such as Jean Leray, Jean Dieudonné, Laurent Schwartz (Fields Medal 1950), Jean-Pierre Serre (Fields Medal 1954), Alexander Grothendieck (Fields Medal 1966) and Jacques-Louis Lions. The Partial differential equations (PDE) team is one of the four research groups of the IECL. It gathers around 30 permanent researchers in different aspects of the PDEs, from theoretical research to numerical analysis and scientific computing. Recent developments in scientific computing at IECL has led to numerous industrial collaborations.

Where to apply

E-mail miha.zaloznik@univ-lorraine.fr

Requirements

Research Field Physics » Computational physics

Education Level Master Degree or equivalent

Research Field Mathematics » Applied mathematics

Education Level Master Degree or equivalent

Research Field Engineering » Materials engineering

Education Level Master Degree or equivalent

Skills/Qualifications

The funding is open to excellent students from physics, applied mathematics, mechanical/chemical/process engineering or other disciplines. We are looking for candidates with:

• Solid background in numerical methods and machine learning.
• Proficiency in technical report writing and presentation.
• Excellent capacity for teamwork, sense of initiative, and ability to work in a multidisciplinary environment.
• Fluent in English, some knowledge of French is beneficial.

Languages

ENGLISH Level Excellent

FRENCH Level Basic

Research Field Physics » Computational physics

Research Field Mathematics » Applied mathematics

Research Field Engineering » Materials engineering

Years of Research Experience None

Additional Information

Selection process

Eligible applicants will be interviewed by an ad hoc committee after receipt of the application. The selected candidate will be interviewed in May 2025 by a committee of the funding body - the ENACT AI cluster (https://cluster-ia-enact.ai). The notification on funding will be communicated in early June.

Additional comments

Institut Jean Lamour (IJL) falls under a Zone à régime restrictif (ZRR). The selected applicants will be subject to a Security Clearance check, required for employment at IJL.