Physics informed machine learning: Seismic wave equation

Similar to many fields of sciences,recent deep learning advances have been applied extensively in geosciences for both small-and large-scale problems.However,the necessity of using large training data and the’black box’nature of learning have limited them in practice and difficult to interpret.Furthermore,including the governing equations and physical facts in such methods is also another challenge,which entails either ignoring the physics or simplifying them using unrealistic data.To address such issues,physics informed machine learning methods have been developed which can integrate the governing physics law into the learning process.In this work,a 1-dimensional(1 D)time-dependent seismic wave equation is considered and solved using two methods,namely Gaussian process(GP)and physics informed neural networks.We show that these meshless methods are trained by smaller amount of data and can predict the solution of the equation with even high accuracy.They are also capable of inverting any parameter involved in the governing equation such as wave velocity in our case.Results show that the GP can predict the solution of the seismic wave equation with a lower level of error,while our developed neural network is more accurate for velocity(P-and S-wave)and density inversion.

FIRST LANGUAGE ACQUISITION AS A MODEL FOR SECOND LANGUAGE ACQUISITION: THE TOTAL PHYSICAL RESPONSE APPROACH IN SECOND LANGUAGE LEARNING AND TEACHING

L1 and L2 acquisition, in some respects, are similar. Language development in children goes hand in hand with physical and cognitive development. Children learn their first language by imitation, but not always and not only by imitation. There seems to be some "innate capacities" that make children start to speak at the same time they do and in the way they do it. Adults learning a second language usually are controlled more by their motivation. But language input is important for both L1 and L2 acquisition. Though there are differences between CL1 and between CL2 and AL2, the way in which these learners acquire some of the grammatical morphemes is similar. This, together with some other evidence, shows that it is not only children who can acquire language. Adults can also acquire a language. But when adults acquire a language, they should also learn it. Some of the ways in which children acquire their language can be used as a model for L2 acquisition, even for Chinese students whose language is unrelated to English and whose culture is different. Learning the culture of the English-speaking countries will benefit the learning of the language. Like children, listening should also be well in advance of speaking in L2 acquisition. To train listening comprehension skills, Asher’s TPR approach proves more effective. TPR approach is at the moment limited to the beginning stage only. In order for students to gain all the five skills in a second language learning, namely, listening, speaking, reading, writing, and interpreting/translating, other methods should be used at the same time, or at later stages.

Implementing physically active learning:Future directions for research,policy,and practice

Purpose:To identify co-produced multi-stakeholder perspectives important for successful widespread physically active learning(PAL) adoption and implementation.Methods:A total of 35 stakeholders(policymakers n=9;commercial education sector,n=8;teachers,n=3;researchers,n=15) attended a design thinking PAL workshop.Participants formed 5 multi-disciplinary groups with at least 1 representative from each stakeholder group.Each group,facilitated by a researcher,undertook 2 tasks:(1) using Post-it Notes,the following question was answered:within the school day,what are the opportunities for learning combined with movement?and(2) structured as a washing-line task,the following question was answered:how can we establish PAL as the norm?All discussions were audio-recorded and transcribed.Inductive analyses were conducted by 4 authors.After the analyses were complete,the main themes and subthemes were assigned to 4 predetermined categories:(1) PAL design and implementation,(2) priorities for practice,(3) priorities for policy,and(4) priorities for research.Results:The following were the main themes for PAL implementation:opportunities for PAL within the school day,delivery environments,learning approaches,and the intensity of PAL.The main themes for the priorities for practice included teacher confidence and competence,resources to support delivery,and community of practice.The main themes for the policy for priorities included self-governance,the Office for Standards in Education,Children’s Services,and Skill,policy investment in initial teacher training,and curriculum reform.The main themes for the research priorities included establishing a strong evidence base,school-based PAL implementation,and a whole-systems approach.Conclusion:The present study is the first to identify PAL implementation factors using a combined multi-stakeholder perspective.To achieve wider PAL adoption and implementation,future interventions should be evidence based and address implementation factors at the classroom level(e.g.,approaches and delivery environments),school level(e.g.,communities of practice),and policy level(e.g.,initial teacher training).

Physical neural networks with self-learning capabilities

Physical neural networks are artificial neural networks that mimic synapses and neurons using physical systems or materials.These networks harness the distinctive characteristics of physical systems to carry out computations effectively,potentially surpassing the constraints of conventional digital neural networks.A recent advancement known as“physical self-learning”aims to achieve learning through intrinsic physical processes rather than relying on external computations.This article offers a comprehensive review of the progress made in implementing physical self-learning across various physical systems.Prevailing learning strategies that contribute to the realization of physical self-learning are discussed.Despite challenges in understanding the fundamental mechanism of learning,this work highlights the progress towards constructing intelligent hardware from the ground up,incorporating embedded self-organizing and self-adaptive dynamics in physical systems.

Neural Networks with Local Converging Inputs(NNLCI)for Solving Conservation Laws,Part I:1D Problems

A novel neural network method is developed for solving systems of conservation laws whose solutions may contain abrupt changes of state,including shock waves and contact discontinuities.In conventional approaches,a low-cost solution patch is usually used as the input to a neural network for predicting the high-fidelity solution patch.With that technique,however,there is no way to distinguish a smeared discontinuity from a smooth solution with large gradient in the input,and the two almost identical inputs correspond to two fundamentally different high-fidelity solution patches in training and predicting.To circumvent this difficulty,we use local patches of two low-cost numerical solutions of the conservation laws in a converging sequence as the input to a neural network.The neural network then makes a correct prediction by identifying whether the solution contains discontinuities or just smooth variations with large gradients,because the former becomes increasingly steep in a converging sequence in the input,and the latter does not.The inputs can be computed from lowcost numerical schemes with coarse resolution,in a local domain of dependence of a space-time location where the prediction is to be made.Despite smeared input solutions,the output provides sharp approximations of solutions containing shock waves and contact discontinuities.The method works effectively not only for regions with discontinuities,but also for smooth regions of the solution.It is efficient to implement,once trained,and has broader applications for different types of differential equations.

Neural Networks with Local Converging Inputs(NNLCI)for Solving Conservation Laws,Part II:2D Problems

In our prior work[10],neural networks with local converging inputs(NNLCI)were introduced for solving one-dimensional conservation equations.Two solutions of a conservation law in a converging sequence,computed from low-cost numerical schemes,and in a local domain of dependence of the space-time location,were used as the input to a neural network in order to predict a high-fidelity solution at a given space-time location.In the present work,we extend the method to twodimensional conservation systems and introduce different solution techniques.Numerical results demonstrate the validity and effectiveness of the NNLCI method for application to multi-dimensional problems.In spite of low-cost smeared input data,the NNLCI method is capable of accurately predicting shocks,contact discontinuities,and the smooth region of the entire field.The NNLCI method is relatively easy to train because of the use of local solvers.The computing time saving is between one and two orders of magnitude compared with the corresponding high-fidelity schemes for two-dimensional Riemann problems.The relative efficiency of the NNLCI method is expected to be substantially greater for problems with higher spatial dimensions or smooth solutions.