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  1. ; (, 1st workshop on Synergy of Scientific and Machine Learning Modeling, SynS & ML - ICML, Honolulu, Hawaii, USA. July, 2023.)
    PSO-PINN is a class of algorithms for training physics-informed neural networks (PINN) using particle swarm optimization (PSO). PSO-PINN can mitigate the well-known difficulties presented by gradient descent training of PINNs when dealing with PDEs with irregular solutions. Additionally, PSO-PINN is an ensemble approach to PINN that yields reproducible predictions with quantified uncertainty. In this paper, we introduce Multi-Objective PSO-PINN, which treats PINN training as a multi-objective problem. The proposed multi-objective PSO-PINN represents a new paradigm in PINN training, which thus far has relied on scalarizations of the multi-objective loss function. A full multi-objective approach allows on-the-fly compromises in the trade-off among the various components of the PINN loss function. Experimental results with a diffusion PDE problem demonstrate the promise of this methodology. 
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