In the context of science, the well-known adage "a picture is worth a thousand words" might well be "a model is worth a thousand datasets." Scientific models, such as Newtonian physics or biological gene regulatory networks, are human-driven simplifications of complex phenomena that serve as surrogates for the countless experiments that validated the models. Recently, machine learning has been able to overcome the inaccuracies of approximate modeling by directly learning the entire set of nonlinear interactions from data. However, without any predetermined structure from the scientific basis behind the problem, machine learning approaches are flexible but data-expensive, requiring large databases of homogeneous labeled training data. A central challenge is reconciling data that is at odds with simplified models without requiring "big data". 
In this work we develop a new methodology, universal differential equations (UDEs), which augments scientific models with machine-learnable structures for scientifically-based learning. We show how UDEs can be utilized to discover previously unknown governing equations, accurately extrapolate beyond the original data, and accelerate model simulation, all in a time and data-efficient manner. This advance is coupled with open-source software that allows for training UDEs which incorporate physical constraints, delayed interactions, implicitly-defined events, and intrinsic stochasticity in the model. Our examples show how a diverse set of computationally-difficult modeling issues across scientific disciplines, from automatically discovering biological mechanisms to accelerating the training of physics-informed neural networks and large-eddy simulations, can all be transformed into UDE training problems that are efficiently solved by a single software methodology.

/pdf/universal-differential-equations-for-scientific-machine-7df1mbim0x.pdf

Universal Differential Equations for Scientific Machine Learning

Lithium-ion batteries are fuelling the advancing renewable-energy based world. At the core of transformational developments in battery design, modelling and management is data. In this work, the datasets associated with lithium batteries in the public domain are summarised. We review the data by mode of experimental testing, giving particular attention to test variables and data provided. Alongside highlighted tools and platforms, over 30 datasets are reviewed.

Lithium-ion battery data and where to find it

The challenge and opportunity of battery lifetime prediction from field data

Flying car is an effective transport to solve current traffic congestion. The power batteries in flying cars discharge at a high current rate in the takeoff and landing phase, evoking a severe thermal issue. Flat heat pipe (FHP) is a relatively new type of battery thermal management technology, which can effectively maintain the temperature uniformity of the battery pack. We have constructed a resistance‐based thermal model of the batteries considering the impact of the state of charge (SOC), battery temperature, and current on the battery heat generation. The FHP model is developed based on segmental heat conduction model, and integrated into the battery model to form the battery‐FHP‐coupled model for a battery module. Experiments are carried out to verify its accuracy. Then, the battery thermal performance is analyzed under the different discharging conditions including constant discharge rates and dynamic discharge rates for flying cars. Under the condition of the flying cars, the battery maximum temperature appears at the end of takeoff stage, while the maximum temperature difference appears during the forward flight segment. Moreover, different FHP heat dissipation structures are studied to further improve the battery thermal performance. The configuration with the best performance is adopted for the battery pack, and it can meet the heat dissipation requirements of the pack at a discharge rate of 3C or that of flying cars. Finally, the influence of inlet cooling air velocity and temperature on battery thermal performance is investigated. According to the research results, air velocity has little effect on the battery maximum temperature at the discharge rate of flying cars, but it can obviously affect the temperature decrease rate. Besides, the battery maximum temperature and its temperature difference develop linearly with the air temperature.

A novel heat dissipation structure based on flat heat pipe for battery thermal management system

Neural Ordinary Differential Equations (ODEs) are a promising approach to learn dynamical models from time-series data in science and engineering applications. This work aims at learning neural ODEs for stiff systems, which are usually raised from chemical kinetic modeling in chemical and biological systems. We first show the challenges of learning neural ODEs in the classical stiff ODE systems of Robertson’s problem and propose techniques to mitigate the challenges associated with scale separations in stiff systems. We then present successful demonstrations in stiff systems of Robertson’s problem and an air pollution problem. The demonstrations show that the usage of deep networks with rectified activations, proper scaling of the network outputs as well as loss functions, and stabilized gradient calculations are the key techniques enabling the learning of stiff neural ODEs. The success of learning stiff neural ODEs opens up possibilities of using neural ODEs in applications with widely varying time-scales, such as chemical dynamics in energy conversion, environmental engineering, and life sciences.

Stiff neural ordinary differential equations.

Electric mobility application design requires accurate and fast prediction of Li-ion battery performance and life. An emerging area of mobility enabled by electrification is electric vertical takeoff and landing aircraft (eVTOL) for urban air mobility (UAM). Design process, techno-economic analysis and the operation of on-board systems depend on the fast and accurate prediction of Li-ion battery performance and life. These models must be accurate for the unique use-case of UAM requiring high power at takeoff and landing, thereby, causing significant rise in battery cell temperature. In this work, we generate a battery performance and thermal dataset specific to eVTOL use-cases and develop a fast and accurate performance and degradation model around that dataset. We use a machine-learning based physics-informed battery performance model to break the typically observed accuracy-computing cost trade-off. We fit the aging parameters for each cycle in a given cell's lifetime, and then model the evolution of those parameters using a new approach that combines traditional physics-based models, consisting of SEI film growth, charge loss, and Li Plating, along with a neural network in a universal ordinary differential equations (u-ODEs) framework. The new approach provides a unique way to combine the extrapolative capability of physics-based models with the representation power of neural networks.

pdf/universal-battery-performance-and-degradation-model-for-7ekiwjufj7.pdf

Universal Battery Performance and Degradation Model for Electric Aircraft

Electric vertical takeoff and landing aircraft have a unique duty cycle characterized by high discharge currents at the beginning and end of the mission (corresponding to takeoff and landing of the aircraft) and a moderate power requirement between them with no rest periods during the mission. Here, we generated a dataset of battery duty profiles for an electric vertical takeoff and landing aircraft using a cell typical for that application. The dataset features 22 cells, comprising a total of 21,392 charge and discharge cycles. 3 of the cells use the baseline cycle while each of the other cells vary either charge current, discharge power, discharge duration, ambient cooling conditions, or end of charge voltage. While it was designed to mimic the expected duty cycle of an electric aircraft, this dataset is relevant for training machine learning models on battery life, fitting physical or empirical models for battery performance and/or degradation, and countless other applications. 

/pdf/a-battery-dataset-for-electric-vertical-takeoff-and-landing-r3tn8ody.pdf

A battery dataset for electric vertical takeoff and landing aircraft

Negative effects of greenhouse gas emissions from internal combustion engines has motivated a global trend towards electrification of transportation powertrains. Additionally, electrification of vehicle prime movers has enabled novel powertrain configurations such as electric distributed propulsion. Electric vertical take-off and landing (eVTOL) aircraft are a novel transportation mode developed at a confluence of emerging technologies including electric powertrains. eVTOLs are poised to institute a major change to urban mobility by increasing the speed and efficiency of urban travel. To facilitate safe and reliable operations, eVTOL battery packs must reliably provide adequate electrical power for mission requirements while sustaining pack health and cycle life over the course of hundreds of missions. These packs are under considerable thermal stress during flight, and must be designed to meet the challenges caused by these thermal stresses, including keeping individual battery cells below temperature limits. Using system simulation can be instrumental in providing optimal design of battery pack layouts and thermal management strategies. A multi-physics system simulation model has been constructed to predict the electrical-thermal-fluid performance of the A3 Vahana eVTOL battery pack with comparison to test data derived from a notional eVTOL mission profile. The model predicts outputs including individual cell currents, cell temperatures, cell voltage, environmental temperatures, and impact of different thermal management strategies on eVTOL battery pack design. The thermal profile predicted during flight is then passed to a predictive model for battery life using GT-SUITE simulation software. The model is then configured to simulate a thermal runaway event, where one cell is heated to the point of runaway, and response of the pack is predicted under different cooling strategies.

Using Multi-physics System Simulation to Predict Battery Pack Thermal Performance and Risk of Thermal Runaway During eVTOL Aircraft Operations

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Universal Battery Performance and Degradation Model for Electric Aircraft

A battery dataset for electric vertical takeoff and landing aircraft

Using Multi-physics System Simulation to Predict Battery Pack Thermal Performance and Risk of Thermal Runaway During eVTOL Aircraft Operations