Chin Chun Ooi

Nicholas Sung Wei Yong, Jian Cheng Wong, Pao-Hsiung Chiu et al.

The potential of learned models for fundamental scientific research and discovery is drawing increasing attention worldwide. Physics-informed neural networks (PINNs), where the loss function directly embeds governing equations of scientific phenomena, is one of the key techniques at the forefront of recent advances. PINNs are typically trained using stochastic gradient descent methods, akin to their deep learning counterparts. However, analysis in this paper shows that PINNs' unique loss formulations lead to a high degree of complexity and ruggedness that may not be conducive for gradient descent. Unlike in standard deep learning, PINN training requires globally optimum parameter values that satisfy physical laws as closely as possible. Spurious local optimum, indicative of erroneous physics, must be avoided. Hence, neuroevolution algorithms, with their superior global search capacity, may be a better choice for PINNs relative to gradient descent methods. Here, we propose a set of five benchmark problems, with open-source codes, spanning diverse physical phenomena for novel neuroevolution algorithm development. Using this, we compare two neuroevolution algorithms against the commonly used stochastic gradient descent, and our baseline results support the claim that neuroevolution can surpass gradient descent, ensuring better physics compliance in the predicted outputs. %Furthermore, implementing neuroevolution with JAX leads to orders of magnitude speedup relative to standard implementations.

Jian Cheng Wong, Pao-Hsiung Chiu, Chinchun Ooi et al.

We present a novel loss formulation for efficient learning of complex dynamics from governing physics, typically described by partial differential equations (PDEs), using physics-informed neural networks (PINNs). In our experiments, existing versions of PINNs are seen to learn poorly in many problems, especially for complex geometries, as it becomes increasingly difficult to establish appropriate sampling strategy at the near boundary region. Overly dense sampling can adversely impede training convergence if the local gradient behaviors are too complex to be adequately modelled by PINNs. On the other hand, if the samples are too sparse, existing PINNs tend to overfit the near boundary region, leading to incorrect solution. To prevent such issues, we propose a new Boundary Connectivity (BCXN) loss function which provides linear local structure approximation (LSA) to the gradient behaviors at the boundary for PINN. Our BCXN-loss implicitly imposes local structure during training, thus facilitating fast physics-informed learning across entire problem domains with order of magnitude sparser training samples. This LSA-PINN method shows a few orders of magnitude smaller errors than existing methods in terms of the standard L2-norm metric, while using dramatically fewer training samples and iterations. Our proposed LSA-PINN does not pose any requirement on the differentiable property of the networks, and we demonstrate its benefits and ease of implementation on both multi-layer perceptron and convolutional neural network versions as commonly used in current PINN literature.

Jian Cheng Wong, Chin Chun Ooi, Joyjit Chattoraj et al.

Computational Intelligence (CI) techniques have shown great potential as a surrogate model of expensive physics simulation, with demonstrated ability to make fast predictions, albeit at the expense of accuracy in some cases. For many scientific and engineering problems involving geometrical design, it is desirable for the surrogate models to precisely describe the change in geometry and predict the consequences. In that context, we develop graph neural networks (GNNs) as fast surrogate models for physics simulation, which allow us to directly train the models on 2/3D geometry designs that are represented by an unstructured mesh or point cloud, without the need for any explicit or hand-crafted parameterization. We utilize an encoder-processor-decoder-type architecture which can flexibly make prediction at both node level and graph level. The performance of our proposed GNN-based surrogate model is demonstrated on 2 example applications: feature designs in the domain of additive engineering and airfoil design in the domain of aerodynamics. The models show good accuracy in their predictions on a separate set of test geometries after training, with almost instant prediction speeds, as compared to O(hour) for the high-fidelity simulations required otherwise.

Kong Yuan Ho, Chin Seng Lim, Matthena A. Kattar et al.

Traffic emissions are known to contribute significantly to air pollution around the world, especially in heavily urbanized cities such as Singapore. It has been previously shown that the particulate pollution along major roadways exhibit strong correlation with increased traffic during peak hours, and that reductions in traffic emissions can lead to better health outcomes. However, in many instances, obtaining proper counts of vehicular traffic remains manual and extremely laborious. This then restricts one's ability to carry out longitudinal monitoring for extended periods, for example, when trying to understand the efficacy of intervention measures such as new traffic regulations (e.g. car-pooling) or for computational modelling. Hence, in this study, we propose and implement an integrated machine learning pipeline that utilizes traffic images to obtain vehicular counts that can be easily integrated with other measurements to facilitate various studies. We verify the utility and accuracy of this pipeline on an open-source dataset of traffic images obtained for a location in Singapore and compare the obtained vehicular counts with collocated particulate measurement data obtained over a 2-week period in 2022. The roadside particulate emission is observed to correlate well with obtained vehicular counts with a correlation coefficient of 0.93, indicating that this method can indeed serve as a quick and effective correlate of particulate emissions.

Jordon Kho, Winston Koh, Jian Cheng Wong et al.

Reaction-diffusion (Turing) systems are fundamental to the formation of spatial patterns in nature and engineering. These systems are governed by a set of non-linear partial differential equations containing parameters that determine the rate of constituent diffusion and reaction. Critically, these parameters, such as diffusion coefficient, heavily influence the mode and type of the final pattern, and quantitative characterization and knowledge of these parameters can aid in bio-mimetic design or understanding of real-world systems. However, the use of numerical methods to infer these parameters can be difficult and computationally expensive. Typically, adjoint solvers may be used, but they are frequently unstable for very non-linear systems. Alternatively, massive amounts of iterative forward simulations are used to find the best match, but this is extremely effortful. Recently, physics-informed neural networks have been proposed as a means for data-driven discovery of partial differential equations, and have seen success in various applications. Thus, we investigate the use of physics-informed neural networks as a tool to infer key parameters in reaction-diffusion systems in the steady-state for scientific discovery or design. Our proof-of-concept results show that the method is able to infer parameters for different pattern modes and types with errors of less than 10\%. In addition, the stochastic nature of this method can be exploited to provide multiple parameter alternatives to the desired pattern, highlighting the versatility of this method for bio-mimetic design. This work thus demonstrates the utility of physics-informed neural networks for inverse parameter inference of reaction-diffusion systems to enhance scientific discovery and design.

Jian Cheng Wong, Pao-Hsiung Chiu, Chin Chun Ooi et al.

Physics-Informed Neural Networks (PINNs) have been shown to be an effective way of incorporating physics-based domain knowledge into neural network models for many important real-world systems. They have been particularly effective as a means of inferring system information based on data, even in cases where data is scarce. Most of the current work however assumes the availability of high-quality data. In this work, we further conduct a preliminary investigation of the robustness of physics-informed neural networks to the magnitude of noise in the data. Interestingly, our experiments reveal that the inclusion of physics in the neural network is sufficient to negate the impact of noise in data originating from hypothetical low quality sensors with high signal-to-noise ratios of up to 1. The resultant predictions for this test case are seen to still match the predictive value obtained for equivalent data obtained from high-quality sensors with potentially 10x less noise. This further implies the utility of physics-informed neural network modeling for making sense of data from sensor networks in the future, especially with the advent of Industry 4.0 and the increasing trend towards ubiquitous deployment of low-cost sensors which are typically noisier.

Shi Jer Low, Venugopalan, S. G. Raghavan et al.

Data-driven approaches, including deep learning, have shown great promise as surrogate models across many domains. These extend to various areas in sustainability. An interesting direction for which data-driven methods have not been applied much yet is in the quick quantitative evaluation of urban layouts for planning and design. In particular, urban designs typically involve complex trade-offs between multiple objectives, including limits on urban build-up and/or consideration of urban heat island effect. Hence, it can be beneficial to urban planners to have a fast surrogate model to predict urban characteristics of a hypothetical layout, e.g. pedestrian-level wind velocity, without having to run computationally expensive and time-consuming high-fidelity numerical simulations. This fast surrogate can then be potentially integrated into other design optimization frameworks, including generative models or other gradient-based methods. Here we present the use of CNNs for urban layout characterization that is typically done via high-fidelity numerical simulation. We further apply this model towards a first demonstration of its utility for data-driven pedestrian-level wind velocity prediction. The data set in this work comprises results from high-fidelity numerical simulations of wind velocities for a diverse set of realistic urban layouts, based on randomized samples from a real-world, highly built-up urban city. We then provide prediction results obtained from the trained CNN, demonstrating test errors of under 0.1 m/s for previously unseen urban layouts. We further illustrate how this can be useful for purposes such as rapid evaluation of pedestrian wind velocity for a potential new layout. It is hoped that this data set will further accelerate research in data-driven urban AI, even as our baseline model facilitates quantitative comparison to future methods.

Tingyang Wei, Jiao Liu, Abhishek Gupta et al.

Many real-world applications require solving families of expensive multi-objective optimization problems~(EMOPs) under varying operational conditions. This gives rise to parametric expensive multi-objective optimization problems (P-EMOPs) where each task parameter defines a distinct optimization instance. Current multi-objective Bayesian optimization methods have been widely used for finding finite sets of Pareto optimal solutions for individual tasks. However, P-EMOPs present a fundamental challenge: the continuous task parameter space can contain infinite distinct problems, each requiring separate expensive evaluations. This demands learning an inverse model that can directly predict optimized solutions for any task-preference query without expensive re-evaluation. This paper introduces the first parametric multi-objective Bayesian optimizer that learns this inverse model by alternating between (1) acquisition-driven search leveraging inter-task synergies and (2) generative solution sampling via conditional generative models. This approach enables efficient optimization across related tasks and finally achieves direct solution prediction for unseen parameterized EMOPs without additional expensive evaluations. We theoretically justify the faster convergence by leveraging inter-task synergies through task-aware Gaussian processes. Meanwhile, empirical studies in synthetic and real-world benchmarks further verify the effectiveness of our alternating framework.

Tingkai Xue, Chin Chun Ooi, Zhengwei Ge et al.

Numerical simulations provide key insights into many physical, real-world problems. However, while these simulations are solved on a full 3D domain, most analysis only require a reduced set of metrics (e.g. plane-level concentrations). This work presents a hybrid physics-neural model that predicts scalar transport in a complex domain orders of magnitude faster than the 3D simulation (from hours to less than 1 min). This end-to-end differentiable framework jointly learns the physical model parameterization (i.e. orthotropic diffusivity) and a non-Markovian neural closure model to capture unresolved, 'coarse-grained' effects, thereby enabling stable, long time horizon rollouts. This proposed model is data-efficient (learning with 26 training data), and can be flexibly extended to an out-of-distribution scenario (with a moving source), achieving a Spearman correlation coefficient of 0.96 at the final simulation time. Overall results show that this differentiable physics-neural framework enables fast, accurate, and generalizable coarse-grained surrogates for physical phenomena.

Jian Cheng Wong, Chin Chun Ooi, Abhishek Gupta et al.

Physics-informed neural networks (PINNs) are at the forefront of scientific machine learning, making possible the creation of machine intelligence that is cognizant of physical laws and able to accurately simulate them. However, today's PINNs are often trained for a single physics task and require computationally expensive re-training for each new task, even for tasks from similar physics domains. To address this limitation, this paper proposes a pioneering approach to advance the generalizability of PINNs through the framework of Baldwinian evolution. Drawing inspiration from the neurodevelopment of precocial species that have evolved to learn, predict and react quickly to their environment, we envision PINNs that are pre-wired with connection strengths inducing strong biases towards efficient learning of physics. A novel two-stage stochastic programming formulation coupling evolutionary selection pressure (based on proficiency over a distribution of physics tasks) with lifetime learning (to specialize on a sampled subset of those tasks) is proposed to instantiate the Baldwin effect. The evolved Baldwinian-PINNs demonstrate fast and physics-compliant prediction capabilities across a range of empirically challenging problem instances with more than an order of magnitude improvement in prediction accuracy at a fraction of the computation cost compared to state-of-the-art gradient-based meta-learning methods. For example, when solving the diffusion-reaction equation, a 70x improvement in accuracy was obtained while taking 700x less computational time. This paper thus marks a leap forward in the meta-learning of PINNs as generalizable physics solvers. Sample codes are available at https://github.com/chiuph/Baldwinian-PINN.

Zhao Wei, Chin Chun Ooi, Abhishek Gupta et al.

This paper presents an evolvable conditional diffusion method such that black-box, non-differentiable multi-physics models, as are common in domains like computational fluid dynamics and electromagnetics, can be effectively used for guiding the generative process to facilitate autonomous scientific discovery. We formulate the guidance as an optimization problem where one optimizes for a desired fitness function through updates to the descriptive statistic for the denoising distribution, and derive an evolution-guided approach from first principles through the lens of probabilistic evolution. Interestingly, the final derived update algorithm is analogous to the update as per common gradient-based guided diffusion models, but without ever having to compute any derivatives. We validate our proposed evolvable diffusion algorithm in two AI for Science scenarios: the automated design of fluidic topology and meta-surface. Results demonstrate that this method effectively generates designs that better satisfy specific optimization objectives without reliance on differentiable proxies, providing an effective means of guidance-based diffusion that can capitalize on the wealth of black-box, non-differentiable multi-physics numerical models common across Science.

Jian Cheng Wong, Abhishek Gupta, Chin Chun Ooi et al.

Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically expressible laws of nature into their training loss function. By complying with physical laws, PINNs provide advantages over purely data-driven models in limited-data regimes and present as a promising route towards Physical AI. This feature has propelled them to the forefront of scientific machine learning, a domain characterized by scarce and costly data. However, the vision of accurate physics-informed learning comes with significant challenges. This work examines PINNs in terms of model optimization and generalization, shedding light on the need for new algorithmic advances to overcome issues pertaining to the training speed, precision, and generalizability of today's PINN models. Of particular interest are gradient-free evolutionary algorithms (EAs) for optimizing the uniquely complex loss landscapes arising in PINN training. Methods synergizing gradient descent and EAs for discovering bespoke neural architectures and balancing multiple terms in physics-informed learning objectives are positioned as important avenues for future research. Another exciting track is to cast EAs as a meta-learner of generalizable PINN models. To substantiate these proposed avenues, we further highlight results from recent literature to showcase the early success of such approaches in addressing the aforementioned challenges in PINN optimization and generalization.

Zhao Wei, Chin Chun Ooi, Yew-Soon Ong

Neural architecture search (NAS) is an attractive approach to automate the design of optimized architectures but is constrained by high computational budget, especially when optimizing for multiple, important conflicting objectives. To address this, an adaptive Co-Kriging-assisted multi-fidelity multi-objective NAS algorithm is proposed to further reduce the computational cost of NAS by incorporating a clustering-based local multi-fidelity infill sampling strategy, enabling efficient exploration of the search space for faster convergence. This algorithm is further accelerated by the use of a novel continuous encoding method to represent the connections of nodes in each cell within a generalized cell-based U-Net backbone, thereby decreasing the search dimension (number of variables). Results indicate that the proposed NAS algorithm outperforms previously published state-of-the-art methods under limited computational budget on three numerical benchmarks, a 2D Darcy flow regression problem and a CHASE_DB1 biomedical image segmentation problem. The proposed method is subsequently used to create a wind velocity regression model with application in urban modelling, with the found model able to achieve good prediction with less computational complexity. Further analysis revealed that the NAS algorithm independently identified principles undergirding superior U-Net architectures in other literature, such as the importance of allowing each cell to incorporate information from prior cells.

Nigel Yuan Yun Ng, Harish Gopalan, Venugopalan S. G. Raghavan et al.

Numerical weather prediction (NWP) and machine learning (ML) methods are popular for solar forecasting. However, NWP models have multiple possible physical parameterizations, which requires site-specific NWP optimization. This is further complicated when regional NWP models are used with global climate models with different possible parameterizations. In this study, an alternative approach is proposed and evaluated for four radiation models. Weather Research and Forecasting (WRF) model is run in both global and regional mode to provide an estimate for solar irradiance. This estimate is then post-processed using ML to provide a final prediction. Normalized root-mean-square error from WRF is reduced by up to 40-50% with this ML error correction model. Results obtained using CAM, GFDL, New Goddard and RRTMG radiation models were comparable after this correction, negating the need for WRF parameterization tuning. Other models incorporating nearby locations and sensor data are also evaluated, with the latter being particularly promising.

Pao-Hsiung Chiu, Jian Cheng Wong, Chinchun Ooi et al.

In this study, novel physics-informed neural network (PINN) methods for coupling neighboring support points and their derivative terms which are obtained by automatic differentiation (AD), are proposed to allow efficient training with improved accuracy. The computation of differential operators required for PINNs loss evaluation at collocation points are conventionally obtained via AD. Although AD has the advantage of being able to compute the exact gradients at any point, such PINNs can only achieve high accuracies with large numbers of collocation points, otherwise they are prone to optimizing towards unphysical solution. To make PINN training fast, the dual ideas of using numerical differentiation (ND)-inspired method and coupling it with AD are employed to define the loss function. The ND-based formulation for training loss can strongly link neighboring collocation points to enable efficient training in sparse sample regimes, but its accuracy is restricted by the interpolation scheme. The proposed coupled-automatic-numerical differentiation framework, labeled as can-PINN, unifies the advantages of AD and ND, providing more robust and efficient training than AD-based PINNs, while further improving accuracy by up to 1-2 orders of magnitude relative to ND-based PINNs. For a proof-of-concept demonstration of this can-scheme to fluid dynamic problems, two numerical-inspired instantiations of can-PINN schemes for the convection and pressure gradient terms were derived to solve the incompressible Navier-Stokes (N-S) equations. The superior performance of can-PINNs is demonstrated on several challenging problems, including the flow mixing phenomena, lid driven flow in a cavity, and channel flow over a backward facing step. The results reveal that for challenging problems like these, can-PINNs can consistently achieve very good accuracy whereas conventional AD-based PINNs fail.

Quang Tuyen Le, Pao-Hsiung Chiu, Chin Chun Ooi

Microfluidics have shown great promise in multiple applications, especially in biomedical diagnostics and separations. While the flow properties of these microfluidic devices can be solved by numerical methods such as computational fluid dynamics (CFD), the process of mesh generation and setting up a numerical solver requires some domain familiarity, while more intuitive commercial programs such as Fluent and StarCCM can be expensive. Hence, in this work, we demonstrated the use of a U-Net convolutional neural network as a surrogate model for predicting the velocity and pressure fields that would result for a particular set of microfluidic filter designs. The surrogate model is fast, easy to set-up and can be used to predict and assess the flow velocity and pressure fields across the domain for new designs of interest via the input of a geometry-encoding matrix. In addition, we demonstrate that the same methodology can also be used to train a network to predict pressure based on velocity data, and propose that this can be an alternative to numerical algorithms for calculating pressure based on velocity measurements from particle-image velocimetry measurements. Critically, in both applications, we demonstrate prediction test errors of less than 1%, suggesting that this is indeed a viable method.

Quang Tuyen Le, Chin Chun Ooi

Algebraic or geometric multigrid methods are commonly used in numerical solvers as they are a multi-resolution method able to handle problems with multiple scales. In this work, we propose a modification to the commonly-used U-Net neural network architecture that is inspired by the principles of multigrid methods, referred to here as U-Net-MG. We then demonstrate that this proposed U-Net-MG architecture can successfully reduce the test prediction errors relative to the conventional U-Net architecture when modeling a set of fluid dynamic problems. In total, we demonstrate an improvement in the prediction of velocity and pressure fields for the canonical fluid dynamics cases of flow past a stationary cylinder, flow past 2 cylinders in out-of-phase motion, and flow past an oscillating airfoil in both the propulsion and energy harvesting modes. In general, while both the U-Net and U-Net-MG models can model the systems well with test RMSEs of less than 1%, the use of the U-Net-MG architecture can further reduce RMSEs by between 20% and 70%.