What's Next? Predicting Hamiltonian Dynamics from Discrete Observations of a Vector Field

We present several methods for predicting the dynamics of Hamiltonian systems from discrete observations of their vector field. Each method is either informed or uninformed of the Hamiltonian property. We empirically and comparatively evaluate the methods and observe that information that the system is Hamiltonian can be effectively informed, and that different methods strike different trade-offs between efficiency and effectiveness for different dynamical systems.Comment: v1: long paper v2: accepted paper (short paper

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

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

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

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

Pan-cancer analysis of whole genomes

Cancer is driven by genetic change, and the advent of massively parallel sequencing has enabled systematic documentation of this variation at the whole-genome scale(1-3). Here we report the integrative analysis of 2,658 whole-cancer genomes and their matching normal tissues across 38 tumour types from the Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium of the International Cancer Genome Consortium (ICGC) and The Cancer Genome Atlas (TCGA). We describe the generation of the PCAWG resource, facilitated by international data sharing using compute clouds. On average, cancer genomes contained 4-5 driver mutations when combining coding and non-coding genomic elements; however, in around 5% of cases no drivers were identified, suggesting that cancer driver discovery is not yet complete. Chromothripsis, in which many clustered structural variants arise in a single catastrophic event, is frequently an early event in tumour evolution; in acral melanoma, for example, these events precede most somatic point mutations and affect several cancer-associated genes simultaneously. Cancers with abnormal telomere maintenance often originate from tissues with low replicative activity and show several mechanisms of preventing telomere attrition to critical levels. Common and rare germline variants affect patterns of somatic mutation, including point mutations, structural variants and somatic retrotransposition. A collection of papers from the PCAWG Consortium describes non-coding mutations that drive cancer beyond those in the TERT promoter(4); identifies new signatures of mutational processes that cause base substitutions, small insertions and deletions and structural variation(5,6); analyses timings and patterns of tumour evolution(7); describes the diverse transcriptional consequences of somatic mutation on splicing, expression levels, fusion genes and promoter activity(8,9); and evaluates a range of more-specialized features of cancer genomes(8,10-18).Peer reviewe

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

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