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Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs). Concurrently, topological descriptors based on persistent homology (PH) are being increasingly employed to augment the GNNs. We investigate the benefits of integrating these two paradigms. Specifically, we introduce TopNets as a broad framework that subsumes and unifies various methods in the intersection of GNNs/TNNs and PH such as (generalizations of) RePHINE and TOGL. TopNets can also be readily adapted to handle (symmetries in) geometric complexes, extending the scope of TNNs and PH to spatial settings. Theoretically, we show that PH descriptors can provably enhance the expressivity of simplicial message-passing networks. Empirically, (continuous and E(n)-equivariant extensions of) TopNets achieve strong performance across diverse tasks, including antibody design, molecular dynamics simulation, and drug property prediction., Comment: Accepted to ICML 2024

Climate and weather prediction traditionally relies on complex numerical simulations of atmospheric physics. Deep learning approaches, such as transformers, have recently challenged the simulation paradigm with complex network forecasts. However, they often act as data-driven black-box models that neglect the underlying physics and lack uncertainty quantification. We address these limitations with ClimODE, a spatiotemporal continuous-time process that implements a key principle of advection from statistical mechanics, namely, weather changes due to a spatial movement of quantities over time. ClimODE models precise weather evolution with value-conserving dynamics, learning global weather transport as a neural flow, which also enables estimating the uncertainty in predictions. Our approach outperforms existing data-driven methods in global and regional forecasting with an order of magnitude smaller parameterization, establishing a new state of the art., Comment: Accepted as ICLR 2024 Oral. Project website: https://yogeshverma1998.github.io/ClimODE/

This work introduces FMG, a field-based model for drug-like molecule generation. We show how the flexibility of this method provides crucial advantages over the prevalent, point-cloud based methods, and achieves competitive molecular stability generation. We tackle optical isomerism (enantiomers), a previously omitted molecular property that is crucial for drug safety and effectiveness, and thus account for all molecular geometry aspects. We demonstrate how previous methods are invariant to a group of transformations that includes enantiomer pairs, leading them invariant to the molecular R and S configurations, while our field-based generative model captures this property., Comment: 15 pages, 14 figures

Antibodies are Y-shaped proteins that neutralize pathogens and constitute the core of our adaptive immune system. De novo generation of new antibodies that target specific antigens holds the key to accelerating vaccine discovery. However, this co-design of the amino acid sequence and the 3D structure subsumes and accentuates some central challenges from multiple tasks, including protein folding (sequence to structure), inverse folding (structure to sequence), and docking (binding). We strive to surmount these challenges with a new generative model AbODE that extends graph PDEs to accommodate both contextual information and external interactions. Unlike existing approaches, AbODE uses a single round of full-shot decoding and elicits continuous differential attention that encapsulates and evolves with latent interactions within the antibody as well as those involving the antigen. We unravel fundamental connections between AbODE and temporal networks as well as graph-matching networks. The proposed model significantly outperforms existing methods on standard metrics across benchmarks., Comment: Accepted at ICML 2023

Generating new molecules is fundamental to advancing critical applications such as drug discovery and material synthesis. Flows can generate molecules effectively by inverting the encoding process, however, existing flow models either require artifactual dequantization or specific node/edge orderings, lack desiderata such as permutation invariance, or induce discrepancy between the encoding and the decoding steps that necessitates post hoc validity correction. We circumvent these issues with novel continuous normalizing E(3)-equivariant flows, based on a system of node ODEs coupled as a graph PDE, that repeatedly reconcile locally toward globally aligned densities. Our models can be cast as message-passing temporal networks, and result in superlative performance on the tasks of density estimation and molecular generation. In particular, our generated samples achieve state-of-the-art on both the standard QM9 and ZINC250K benchmarks., Comment: Accepted to NeurIPS 2022. More info at: https://yogeshverma1998.github.io/ModFlow/

Pions constitute nearly $70\%$ of final state particles in ultra high energy collisions. They act as a probe to understand the statistical properties of Quantum Chromodynamics (QCD) matter i.e. Quark Gluon Plasma (QGP) created in such relativistic heavy ion collisions (HIC). Apart from this, direct photons are the most versatile tools to study relativistic HIC. They are produced, by various mechanisms, during the entire space-time history of the strongly interacting system. Direct photons provide measure of jet-quenching when compared with other quark or gluon jets. The $\pi^{0}$ decay into two photons make the identification of non-correlated gamma coming from another process cumbersome in the Electromagnetic Calorimeter. We investigate the use of deep learning architecture for reconstruction and identification of single as well as multi particles showers produced in calorimeter by particles created in high energy collisions. We utilize the data of electromagnetic shower at calorimeter cell-level to train the network and show improvements for identification and characterization. These networks are fast and computationally inexpensive for particle shower identification and reconstruction for current and future experiments at particle colliders.

The identification of jets and their constituents is one of the key problems and challenging task in heavy ion experiments such as experiments at RHIC and LHC. The presence of huge background of soft particles pose a curse for jet finding techniques. The inabilities or lack of efficient techniques to filter out the background lead to a fake or combinatorial jet formation which may have an errorneous interpretation. In this article, we present Graph Reduction technique (GraphRed), a novel class of physics-aware and topology-based attention graph neural network built upon jet physics in heavy ion collisions. This approach directly works with the physical observables of variable-length set of final state particles on an event-by-event basis to find most likely jet-induced particles in an event. This technique demonstrate the robustness and applicability of this method for finding jet-induced particles and show that graph architectures are more efficient than previous frameworks. This technique exhibit foremost time a classifier working on particle-level in each heavy ion event produced at the LHC. We present the applicability and integration of the model with current jet finding algorithms such as FastJet.

Muons are the most abundant charged particles arriving at sea level originating from the decay of secondary charged pions and kaons. These secondary particles are created when high-energy cosmic rays hit the atmosphere interacting with air nuclei initiating cascades of secondary particles which led to the formation of extensive air showers (EAS). They carry essential information about the extra-terrestrial events and are characterized by large flux and varying angular distribution. To account for open questions and the origin of cosmic rays, one needs to study various components of cosmic rays with energy and arriving direction. Because of the close relation between muon and neutrino production, it is the most important particle to keep track of. We propose a novel tracking algorithm based on the Geometric Deep Learning approach using graphical structure to incorporate domain knowledge to track cosmic ray muons in our 3-D scintillator detector. The detector is modeled using the GEANT4 simulation package and EAS is simulated using CORSIKA (COsmic Ray SImulations for KAscade) with a focus on muons originating from EAS. We shed some light on the performance, robustness towards noise and double hits, limitations, and application of the proposed algorithm in tracking applications with the possibility to generalize to other detectors for astrophysical and collider experiments.