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Understanding thermal stress evolution in metal additive manufacturing (AM) is crucial for producing high-quality components. Recent advancements in machine learning (ML) have shown great potential for modeling complex multiphysics problems in metal AM. While physics-based simulations face the challenge of high computational costs, conventional data-driven ML models require large, labeled training datasets to achieve accurate predictions. Unfortunately, generating large datasets for ML model training through time-consuming experiments or high-fidelity simulations is highly expensive in metal AM. To address these challenges, this study introduces a physics-informed neural network (PINN) framework that incorporates governing physical laws into deep neural networks (NNs) to predict temperature and thermal stress evolution during the laser metal deposition (LMD) process. The study also discusses enhanced accuracy and efficiency of the PINN model when supplemented with small simulation data. Furthermore, it highlights the PINN transferability, enabling fast predictions with a set of new process parameters using a pre-trained PINN model as an online soft sensor, significantly reducing computation time compared to physics-based numerical models while maintaining accuracy. 

Abstract Melt pool dynamics in metal additive manufacturing (AM) is critical to process stability, microstructure formation, and final properties of the printed materials. Physics-based simulation, including computational fluid dynamics (CFD), is the dominant approach to predict melt pool dynamics. However, the physics-based simulation approaches suffer from the inherent issue of very high computational cost. This paper provides a physics-informed machine learning method by integrating the conventional neural networks with the governing physical laws to predict the melt pool dynamics, such as temperature, velocity, and pressure, without using any training data on velocity and pressure. This approach avoids solving the nonlinear Navier–Stokes equation numerically, which significantly reduces the computational cost (if including the cost of velocity data generation). The difficult-to-determine parameters' values of the governing equations can also be inferred through data-driven discovery. In addition, the physics-informed neural network (PINN) architecture has been optimized for efficient model training. The data-efficient PINN model is attributed to the extra penalty by incorporating governing PDEs, initial conditions, and boundary conditions in the PINN model. 

Self-supervised learning through contrastive representations is an emergent and promising avenue, aiming at alleviating the availability of labeled data. Recent research in the field also demonstrates its viability for several downstream tasks, henceforth leading to works that implement the contrastive principle through inno- vative loss functions and methods. However, despite achieving impressive progress, most methods depend on prohibitively large batch sizes and compute requirements for good performance. In this work, we propose the AUC-Contrastive Learning, a new approach to contrastive learning that demonstrates robust and competitive performance in compute-limited regimes. We propose to incorporate the contrastive objective within the AUC-maximization framework, by noting that the AUC metric is maximized upon enhancing the probability of the network’s binary prediction difference between positive and negative samples which inspires adequate embed- ding space arrangements in representation learning. Unlike standard contrastive methods, when performing stochastic optimization, our method maintains unbiased stochastic gradients and thus is more robust to batchsizes as opposed to standard stochastic optimization problems. Remarkably, our method with a batch size of 256, outperforms several state-of-the-art methods that may need much larger batch sizes (e.g., 4096), on ImageNet and other standard datasets. Experiments on transfer learning and few-shot learning tasks also demonstrate the downstream viability of our method. Code is available at AUC-CL. 

Abstract Despite the f₀(980) hadron having been discovered half a century ago, the question about its quark content has not been settled: it might be an ordinary quark-antiquark ($${{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}$) meson, a tetraquark ($${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}q\overline{q}$) exotic state, a kaon-antikaon ($${{\rm{K}}}\overline{{{\rm{K}}}}$$ $K\overline{K}$) molecule, or a quark-antiquark-gluon ($${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{g}}}$$ $q\overline{q}g$) hybrid. This paper reports strong evidence that the f₀(980) state is an ordinary$${{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}$meson, inferred from the scaling of elliptic anisotropies (v₂) with the number of constituent quarks (n_q), as empirically established using conventional hadrons in relativistic heavy ion collisions. The f₀(980) state is reconstructed via its dominant decay channel f₀(980) →π⁺π⁻, in proton-lead collisions recorded by the CMS experiment at the LHC, and itsv₂is measured as a function of transverse momentum (p_T). It is found that then_q= 2 ($${{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}$state) hypothesis is favored overn_q= 4 ($${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}q\overline{q}$or$${{\rm{K}}}\overline{{{\rm{K}}}}$$ $K\overline{K}$states) by 7.7, 6.3, or 3.1 standard deviations in thep_T< 10, 8, or 6 GeV/cranges, respectively, and overn_q= 3 ($${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{g}}}$$ $q\overline{q}g$hybrid state) by 3.5 standard deviations in thep_T< 8 GeV/crange. This result represents the first determination of the quark content of the f₀(980) state, made possible by using a novel approach, and paves the way for similar studies of other exotic hadron candidates.