A Bayesian framework for discovering interpretable Lagrangian of dynamical systems from data

Learning and predicting the dynamics of physical systems requires a profound understanding of the underlying physical laws. Recent works on learning physical laws involve generalizing the equation discovery frameworks to the discovery of Hamiltonian and Lagrangian of physical systems. While the existing methods parameterize the Lagrangian using neural networks, we propose an alternate framework for learning interpretable Lagrangian descriptions of physical systems from limited data using the sparse Bayesian approach. Unlike existing neural network-based approaches, the proposed approach (a) yields an interpretable description of Lagrangian, (b) exploits Bayesian learning to quantify the epistemic uncertainty due to limited data, (c) automates the distillation of Hamiltonian from the learned Lagrangian using Legendre transformation, and (d) provides ordinary (ODE) and partial differential equation (PDE) based descriptions of the observed systems. Six different examples involving both discrete and continuous system illustrates the efficacy of the proposed approach

A foundational neural operator that continuously learns without forgetting

Machine learning has witnessed substantial growth, leading to the development of advanced artificial intelligence models crafted to address a wide range of real-world challenges spanning various domains, such as computer vision, natural language processing, and scientific computing. Nevertheless, the creation of custom models for each new task remains a resource-intensive undertaking, demanding considerable computational time and memory resources. In this study, we introduce the concept of the Neural Combinatorial Wavelet Neural Operator (NCWNO) as a foundational model for scientific computing. This model is specifically designed to excel in learning from a diverse spectrum of physics and continuously adapt to the solution operators associated with parametric partial differential equations (PDEs). The NCWNO leverages a gated structure that employs local wavelet experts to acquire shared features across multiple physical systems, complemented by a memory-based ensembling approach among these local wavelet experts. This combination enables rapid adaptation to new challenges. The proposed foundational model offers two key advantages: (i) it can simultaneously learn solution operators for multiple parametric PDEs, and (ii) it can swiftly generalize to new parametric PDEs with minimal fine-tuning. The proposed NCWNO is the first foundational operator learning algorithm distinguished by its (i) robustness against catastrophic forgetting, (ii) the maintenance of positive transfer for new parametric PDEs, and (iii) the facilitation of knowledge transfer across dissimilar tasks. Through an extensive set of benchmark examples, we demonstrate that the NCWNO can outperform task-specific baseline operator learning frameworks with minimal hyperparameter tuning at the prediction stage. We also show that with minimal fine-tuning, the NCWNO performs accurate combinatorial learning of new parametric PDEs

Mg-MOF-74@SBA-15 hybrids: synthesis, characterization, and adsorption properties

Nanocrystals of Mg-MOF-74 have been immobilized into the mesopores of SBA-15 rods to fabricate Mg-MOF-74@SBA-15 hybrid materials. To furnish such composites, a relatively simple synthetic strategy has been adopted by direct dispersion of the metal-organic framework (MOF) precursors in SBA-15 matrix to prepare the hybrid materials in situ. The hybrid materials have been characterized using powder X-ray diffraction and several spectroscopic and microscopic techniques, which suggest growth of the MOF nanocrystals inside the SBA-15 mesopores and the composites exhibit characteristics of both the components. N2 adsorption isotherms at 77 K reveal that the composites contain additional mesopores, compared to only micropores of pristine MOF nanocrystals. In addition to such combination of both micro and mesoporosity, the composites also demonstrate significant CO2 adsorption at room temperature

Structural diversities in metal-organic coordination polymers based on flexibility in organic spacer

Metal-organic coordination polymers with their various novel structural motifs have drawn intense research interests over the last few decades. Interestingly, flexibility of the organic spacers in such metalorganic coordination polymers can direct various structural topology and intricate networks. A novel 1D coordination polymer and some other illustrative examples with different flexible ligands like 1,2-bis(4-pyridyl)ethane (bpe) and 1,3-bis(4-pyridyl)propane (bpp) have been discussed in this review. Both gauche and anti-conformations could be adopted by the bpe ligand, and hence diverse structures can be furnished. Further flexibility could be achieved by exploiting longer ligand like 1,3-bis(4-pyridyl) propane (bpp). Our group has been pursuing research to furnish such flexible compounds and study their different functionalities. An account of design of such diverse systems by employing judicious ligand design strategy and their different structural aspects will be presented in this review

Multi-fidelity wavelet neural operator with application to uncertainty quantification

Operator learning frameworks, because of their ability to learn nonlinear maps between two infinite dimensional functional spaces and utilization of neural networks in doing so, have recently emerged as one of the more pertinent areas in the field of applied machine learning. Although these frameworks are extremely capable when it comes to modeling complex phenomena, they require an extensive amount of data for successful training which is often not available or is too expensive. However, this issue can be alleviated with the use of multi-fidelity learning, where a model is trained by making use of a large amount of inexpensive low-fidelity data along with a small amount of expensive high-fidelity data. To this end, we develop a new framework based on the wavelet neural operator which is capable of learning from a multi-fidelity dataset. The developed model's excellent learning capabilities are demonstrated by solving different problems which require effective correlation learning between the two fidelities for surrogate construction. Furthermore, we also assess the application of the developed framework for uncertainty quantification. The results obtained from this work illustrate the excellent performance of the proposed framework

Applied Molecular Cloning: Present and Future for Aquaculture

With the grim picture of millions of people living in poverty and hunger, there is also an international alarm over future world food supply. This global concern of food scarcity has established the need to not only increase the production of traditional staples but also fisheries and aquaculture. Genetically, physiologically and phenotypically, fish are the most diverse group of livings. Similar to mammals, molecular biology is being extensively used in aquaculture, be it in disease management, or growth and reproduction enhancement. In this chapter we aim to discuss the molecular methodologies applied to uplift and attain sustainability in aqua farming

Laser-induced fluorescence spectroscopy in supersonic jet and large amplitude motion

Combining supersonic jet techniques with tunable lasers, scientists have been able to obtain precise information on the static and dynamic properties of the molecules in their ground and excited states. The principle of the jet spectroscopies along with application of laser-induced fluorescence technique to large amplitude-vibrational motion has been discussed