Separable Hamiltonian Neural Networks

The modelling of dynamical systems from discrete observations is a challenge faced by modern scientific and engineering data systems. Hamiltonian systems are one such fundamental and ubiquitous class of dynamical systems. Hamiltonian neural networks are state-of-the-art models that unsupervised-ly regress the Hamiltonian of a dynamical system from discrete observations of its vector field under the learning bias of Hamilton's equations. Yet Hamiltonian dynamics are often complicated, especially in higher dimensions where the state space of the Hamiltonian system is large relative to the number of samples. A recently discovered remedy to alleviate the complexity between state variables in the state space is to leverage the additive separability of the Hamiltonian system and embed that additive separability into the Hamiltonian neural network. Following the nomenclature of physics-informed machine learning, we propose three separable Hamiltonian neural networks. These models embed additive separability within Hamiltonian neural networks. The first model uses additive separability to quadratically scale the amount of data for training Hamiltonian neural networks. The second model embeds additive separability within the loss function of the Hamiltonian neural network. The third model embeds additive separability through the architecture of the Hamiltonian neural network using conjoined multilayer perceptions. We empirically compare the three models against state-of-the-art Hamiltonian neural networks, and demonstrate that the separable Hamiltonian neural networks, which alleviate complexity between the state variables, are more effective at regressing the Hamiltonian and its vector field.Comment: 11 page

A Comparative Evaluation of Additive Separability Tests for Physics-Informed Machine Learning

Many functions characterising physical systems are additively separable. This is the case, for instance, of mechanical Hamiltonian functions in physics, population growth equations in biology, and consumer preference and utility functions in economics. We consider the scenario in which a surrogate of a function is to be tested for additive separability. The detection that the surrogate is additively separable can be leveraged to improve further learning. Hence, it is beneficial to have the ability to test for such separability in surrogates. The mathematical approach is to test if the mixed partial derivative of the surrogate is zero; or empirically, lower than a threshold. We present and comparatively and empirically evaluate the eight methods to compute the mixed partial derivative of a surrogate function

Celestial Machine Learning: Discovering the Planarity, Heliocentricity, and Orbital Equation of Mars with AI Feynman

Can a machine or algorithm discover or learn the elliptical orbit of Mars from astronomical sightings alone? Johannes Kepler required two paradigm shifts to discover his First Law regarding the elliptical orbit of Mars. Firstly, a shift from the geocentric to the heliocentric frame of reference. Secondly, the reduction of the orbit of Mars from a three- to a two-dimensional space. We extend AI Feynman, a physics-inspired tool for symbolic regression, to discover the heliocentricity and planarity of Mars' orbit and emulate his discovery of Kepler's first law

Deep learning for chemometric analysis of plastic spectral data from infrared and Raman databases

Increasing plastic recycling rates is key to addressing plastic pollution. New technologies such as chemometric analysis of spectral data have shown great promises in improving the plastic sorting efficiency to boost recycling rates. In this work, a novel deep learning architecture, PolymerSpectraDecisionNet (PSDN) was developed, consisting of convolutional neural networks, residual networks and inception networks in a decision tree structure. To better represent the conditions in the plastic recycling industry, the models were built to identify the most widely recycled polymers – polyethylene, polypropylene and polyethylene terephthalate from open-sourced infrared and Raman spectral dataset containing over 20 different polymers. PSDN performed better than end-to-end neural networks, obtaining an accuracy of 0.949 and 0.967 with the Raman and infrared datasets respectively. The use of deep learning can also distinguish between weathered and unaged polymer samples, with accuracies of 0.954 for high density polyethylene and 0.906 for polyethylene terephthalate

How digitalisation can enable industrial symbiosis practices : a case study

Industrial Symbiosis (IS) encourages a collaborative approach aiming at recovering, reprocessing and reusing non-labour resources and it is a promising solution for mitigating the rising cost of non-labour resource. Introducing IS is a knowledge intensive process and researchers have developed various information and communication (ICT) tools to support the process. However, the use of these tools in the actual industrial practice has not been adequately investigated yet. This study investigates the role that ICT tools play in facilitating the process of creating IS through a case study of International Synergies – the company which facilitated the world’s first national-level IS programme (i.e. NISP UK). Results suggest that the role of digitalisation can increase practitioners’ productivity mainly through data analytics

A collaboration platform for enabling industrial symbiosis : towards creating a self-learning waste-to-resource database for recommending industrial symbiosis transactions using text analytics

Industrial Symbiosis (IS) adopts a collaborative approach, which aims to re-channel resources – traditionally considered spent and non-productive – towards alternative value-adding pathways. Empirically, the concept of IS has been rapidly implemented in practice through a facilitated approach, whereby businesses are engaged and “match-made” via a facilitating body. While recommending alternative pathways for companies to establish IS-based transactions is a long-standing practice, recent technological advancement has shifted the nature of this task from one that is based purely on human intellect and reasoning, towards one which leverages intelligent recommendation algorithms to provide relevant suggestions. Traditionally, these recommendation engines rely on manually populated knowledge bases that are not only labor-intensive to build but also costly to maintain. This work presents the creation of a self-learning waste-to-resource database supporting an IS recommendation system by utilizing text analytics techniques. We further demonstrate its practical application to support IS facilitating bodies in their core activity

Development of a polymer spectral database for advanced chemometric analysis

The use of chemometric techniques with spectral data for sorting plastics to improve recycling rates have gained more attention in recent years. However, insufficient representation of polymer spectra in spectral databases has been one of the barriers to the further development of these techniques. This work aims to develop a polymer spectra dataset that builds upon existing spectral databases on two fronts. Firstly, the data collected includes Laser-induced Breakdown Spectroscopy (LIBS) data in addition to more commonly available Infrared (IR) and Raman data. Secondly, the dataset includes unaged and weathered conditions of the same sample. In total, the dataset includes 732 spectra, with the LIBS, IR and Raman spectra of 122 unique samples, both before and after accelerated weathering. The data collected were qualitatively analyzed and visualized. Further work will explore the effect of using hybrid spectroscopic methods on chemometrics analysis results

Self-Assessment Framework for Corporate Environmental Sustainability in the Era of Digitalization

The shift towards a climate-neutral economy will affect businesses in the upcoming decades. Companies will need to increase their transformation towards environmentally sustainable businesses in the following years, in which digitalization might be a practical enabler to accelerate this transformation. However, as a starting point, companies require knowledge of their current sustainability performance to manage this transition and need a method that provides the necessary information. The use of self-assessment tools is a widely acknowledged method for such processes. Nevertheless, there is a lack of self-assessment tools that integrate sustainability and digitalization perspectives to overcome different organizational barriers. This paper focuses on how managers can be supported in planning their transformations by interlinking sustainability and digitization. Our objective is to enable the managers of companies to assess their current state in terms of corporate environmental sustainability and to explore their policies, information systems, and actions to support their transformation towards sustainable and digital businesses. A self-assessment tool based on a rapid questionnaire is presented after reviewing and synthesizing different approaches, including maturity modeling, sustainability reporting, and digital assessment tools. The self-assessment tool is improved upon evaluation by industry experts and the framework is tested on a case company.</jats:p