In recent years, there has been a growing interest in visualizing the loss landscape of neural networks. Linear landscape visualization methods, such as principal component analysis, have become widely used as they intuitively help researchers study neural networks and their training process. However, these linear methods suffer from limitations and drawbacks due to their lack of flexibility and low fidelity at representing the high dimensional landscape. In this paper, we present a novel auto-encoder-based non-linear landscape visualization method called Neuro-Visualizer that addresses these shortcoming and provides useful insights about neural network loss landscapes. To demonstrate its potential, we run experiments on a variety of problems in two separate applications of knowledge-guided machine learning (KGML). Our findings show that Neuro-Visualizer outperforms other linear and non-linear baselines and helps corroborate, and sometime challenge, claims proposed by machine learning community. All code and data used in the experiments of this paper are available at an anonymous link https://anonymous.4open.science/r/NeuroVisualizer-FDD6

Discovering evolutionary traits that are heritable across species on the tree of life (also referred to as a phylogenetic tree) is of great interest to biologists to understand how organisms diversify and evolve. However, the measurement of traits is often a subjective and labor-intensive process, making trait discovery a highly label-scarce problem. We present a novel approach for discovering evolutionary traits directly from images without relying on trait labels. Our proposed approach, Phylo-NN, encodes the image of an organism into a sequence of quantized feature vectors -- or codes -- where different segments of the sequence capture evolutionary signals at varying ancestry levels in the phylogeny. We demonstrate the effectiveness of our approach in producing biologically meaningful results in a number of downstream tasks including species image generation and species-to-species image translation, using fish species as a target example.

Physics-guided Neural Networks (PGNNs) represent an emerging class of neural networks that are trained using physics-guided (PG) loss functions (capturing violations in network outputs with known physics), along with the supervision contained in data. Existing work in PGNNs have demonstrated the efficacy of adding single PG loss functions in the neural network objectives, using constant trade-off parameters, to ensure better generalizability. However, in the presence of multiple physics loss functions with competing gradient directions, there is a need to adaptively tune the contribution of competing PG loss functions during the course of training to arrive at generalizable solutions. We demonstrate the presence of competing PG losses in the generic neural network problem of solving for the lowest (or highest) eigenvector of a physics-based eigenvalue equation, common to many scientific problems. We present a novel approach to handle competing PG losses and demonstrate its efficacy in learning generalizable solutions in two motivating applications of quantum mechanics and electromagnetic propagation. All the code and data used in this work is available at https://github.com/jayroxis/Cophy-PGNN.