IDS integrates physics engines into deep learning for efficient, interpretable system identification.
problem Lack of generalization and interpretability in learning-based models of physical systems.
method Interactive Differentiable Simulation (IDS) that allows efficient, accurate inference of physical properties.
result Automatic task-based robot design and parameter estimation for nonlinear dynamical systems.
DiffTaichi enables fast, differentiable physical simulations with shorter code.
problem Building efficient differentiable physical simulators.
method Differentiable programming language (DiffTaichi) that generates gradients using source code transformations and a light-weight tape.
result Differentiable physical simulators written in DiffTaichi are faster and more concise than existing methods.
Differentiable pipeline replaces non-differentiable CAE components for shape optimization.
problem Gradient-based optimization is limited by non-differentiable components in CAE workflows.
method Surrogate models replace non-differentiable pipeline components, enabling gradient-based optimization.
result Gradient-based shape optimization possible without differentiable solvers.
A GPU-based workflow for building physics emulators of hypersonic flows
problem Resolving complex physical phenomena in hypersonic flows
method Fully GPU-based workflow integrating accelerated data generation and neural emulators
result Physics emulators remain reliable beyond their training distribution
Survey and new results link hydrodynamics, molecular physics, and financial engineering.
problem Understanding financial engineering topics like Asian options and volatility swaps.
method Linking Kevin waves, Klein-Kramers, and Kolmogorov equations to financial models.
result Corrected the original solution of the Kolmogorov equation.
This work integrates differentiation and integration in Physics-Informed Neural Networks.
problem Solving integro-differential equations and computing integral transforms.
method Augmenting Physics-Informed Neural Networks with automatic integration.
result Solving complex integral transforms and integro-differential equations.
Many processes in science and engineering can be described by partial differential equations (PDEs). Traditionally, PDEs are derived by considering first principles of physics to derive the relations between the involved physical quantities of interest. A different approach is to measure the quantities of interest and …
In this paper, we introduce a physics-driven regularization method for training of deep neural networks (DNNs) for use in engineering design and analysis problems. In particular, we focus on prediction of a physical system, for which in addition to training data, partial or complete information on a set of governing la…
AutoKE automates embedding physical knowledge into neural networks for complex engineering problems.
problem Complex physical equations in engineering problems.
method AutoKE framework using deep neural networks, equation parsing, automatic differentiation, adaptive weights, and NAS.
result Automatically embeds physical knowledge into neural networks for complex equations efficiently.
Paper integrates ML with physics models for engineering and environmental challenges.
problem Complex science and engineering problems require new methodologies combining physics-based models and ML.
method Structured overview of integrating physics-based models with ML techniques.
result Taxonomy of existing techniques and potential research gaps identified.
This work discovers governing equations from limited data using physics-informed deep learning.
problem Discovering governing equations from scarce and noisy data for complex systems.
method Physics-informed deep learning framework integrating neural networks, physics embedding, and sparse regression.
result The method effectively identifies governing equations from various spatiotemporal systems with different levels of data scarcity and noise.
Mathematical advances needed for Digital Twins, differing from traditional models.
problem Foundational mathematical advances required for Digital Twins.
method Multi-scale, multi-physics modeling and coupling, different reliability criteria and uncertainty assessments.
result AI/ML methods can perform well in biomedical problems but fail in simple engineering systems.
Paper presents MF-PIDNN for physics-informed deep learning with low-fidelity data.
problem Challenges in systems with unknown or approximate governing differential equations and limited high-fidelity data.
method Transfer learning between physics-informed and data-driven deep learning models.
result Model provides accurate predictions even in data-scarce regions.
These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous foundation to modern dynamics, as well as field and gauge theories in physics, engi…
New GP model tackles physics constraints efficiently.
problem Lack of efficient, physics-informed models for complex systems.
method Physics-informed variational state-space Gaussian process.
result Efficient spatio-temporal modeling with improved performance.
This work optimizes statistical inference with neural networks for high-energy physics data.
problem Optimal dimensionality reduction with minimal loss of information in the presence of systematic uncertainties.
method Neural network optimization based on binned Poisson likelihoods with nuisance parameters.
result Estimates of parameters of interest close to optimal.
The Spencer operator, introduced by D.C. Spencer fifty years ago, is rarely used in mathematics today and, up to our knowledge, has never been used in engineering applications or mathematical physics. The main purpose of this paper, an extended version of a lecture at the second workshop on Differential Equations by Al…
Physics-informed neural operator learns from coarse to fine discretized data.
problem Lack of high-fidelity training data and uneven grid resolution.
method Physics-informed multi-resolution neural operator framework.
result Learn from arbitrarily discretized input functions using latent embedding and finite difference solver.
TNet combines DL with physics models to solve inverse problems efficiently.
problem Solving inverse problems with limited data and physics constraints.
method Model-constrained deep learning approach using TNet.
result TNet solutions are as accurate as traditional methods but faster.
These lecture notes in the De Rham-Hodge theory are designed for a 1-semester undergraduate course (in mathematics, physics, engineering, chemistry or biology). This landmark theory of the 20th Century mathematics gives a rigorous foundation to modern field and gauge theories in physics, engineering and physiology. The…
DL-PDE discovers PDEs from noisy, sparse data using neural networks and sparse regressions.
problem Discovering PDEs from noisy, sparse data.
method Combines neural networks and sparse regressions to discover PDEs from meta-data generated by a neural network.
result Achieves satisfactory results in real-world engineering settings with noisy and limited data.
Physics-informed WNO learns PDE solutions without labeled data.
problem Data-hungry nature of WNO framework.
method Physics-informed WNO for learning PDE solutions.
result Validated and illustrated with four nonlinear systems.
TgNN improves neural network accuracy for subsurface flow modeling.
problem Improving accuracy of neural network predictions for subsurface flow.
method Theory-guided Neural Network (TgNN) trained with data and physical constraints.
result TgNN achieves higher accuracy and better generalizability than ANN models.
New method uses PINNs to solve complex PDEs with sparse measurements.
problem Joint estimation of source and parameters in advection-diffusion equations with limited data.
method Weighted adaptive approach based on neural tangent kernel of PINNs.
result Successful estimation of source function, velocity, and diffusion parameters.
New method learns SDEs with structured noise from data.
problem Learning SDEs with structured noise from data.
method Nonparametric framework for drift and diffusion terms.
result Accurately infers low-dimensional interaction kernels.
New model uses physics equations to predict complex systems without needing data.
problem Lack of training data for deep learning models of complex systems.
method Physics-constrained deep auto-regressive network.
result Model predicts non-linear dynamical systems with uncertainty quantification.
Enhances neural network solvers for PDEs with complex boundary conditions.
problem Challenges in solving PDEs with high accuracy and complex boundary conditions.
method Integrates natural gradient optimization with numerical time-stepping schemes to enforce Dirichlet boundary conditions.
result Superior accuracy and computational efficiency of the proposed methods for solving PDEs.
DeepONets improve surrogate modeling for engineering systems.
problem Accurately modeling complex PDEs for engineering systems.
method DeepONets specialize in approximating mathematical operators for PDEs.
result DeepONets achieve high prediction accuracy and zero-shot capability.
X-TFC solves parametric DEs with neural networks and physics constraints.
problem Solving parametric differential equations with physics constraints.
method Combines Theory of Functional Connections and Physics-Informed Neural Networks with a single-layer Extreme Learning Machine.
result Achieves high accuracy with low computational time.
Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new class of learnable models--based on graph networks--which implement an inductive…
Machine learning identified 13 key equations for distillation column dynamics.
problem Identify governing laws for complex engineered systems.
method Sparse Identification of Non-Linear Dynamics (SINDy) applied to distillation column data.
result Reduced 1000s of equations to 13 interpretable terms.
Unified framework for forward and inverse PDE problems in multiphase media.
problem Non-differentiable inverse problems in discrete-valued material fields.
method GenPANIS: Latent-variable generative framework preserving discrete microstructures.
result Unified bidirectional inference with minimal labeled pairs and physics-aware decoder.
Unified approach combining BSDEs and PINNs for solving PDEs.
problem Solving high-dimensional partial differential equations.
method Interpolating between BSDEs and PINNs using diffusion loss.
result Unified understanding of numerical approaches for high-dimensional PDEs.
ML predicts alloy properties considering chemistry, processing, and data transformations.
problem Designing and predicting alloy properties in high-dimensional design space.
method Physics-informed machine learning with engineered features from chemistry and heat treatment.
result ML models accurately predict alloy properties, including hysteresis in shape memory alloys.
Hydrodynamics principles applied to finance, solving complex market models.
problem Understanding financial market dynamics using physics principles.
method Unified mathematical framework using Kelvin waves to solve differential and pseudo-differential equations.
result Solved various financial models including volatility and variance swaps.
Residual generation helps diagnose engine faults using neural networks.
problem Fault diagnosis in engines with unknown classes and limited data.
method Grey-box recurrent neural networks incorporating physical insights.
result Improved fault classification and root cause identification.
Maximizing the speed and precision of communication while minimizing power dissipation is a fundamental engineering design goal. Also, biological systems achieve remarkable speed, precision and power efficiency using poorly understood physical design principles. Powerful theories like information theory and thermodynam…
EFiGP uses Fourier and eigen-decomposition for efficient ODE parameter estimation.
problem Parameter estimation and trajectory reconstruction for noisy, sparse, nonlinear ODE systems.
method EFiGP integrates Fourier transformation and eigen-decomposition into a physics-informed Gaussian Process framework.
result EFiGP efficiently estimates ODE parameters and recovers trajectories from noisy data.
Graphical physics network learns intuitive physics using deep reinforcement learning with intrinsic motivation.
problem Teaching intuitive physics to AI agents.
method Integrates deep reinforcement learning with intrinsic reward normalization for efficient learning.
result Agent effectively learns object positions and velocities using intrinsic motivation.
Proposes neural networks for solving complex free boundary problems.
problem Solving free boundary and Stefan problems with complex interfaces.
method Physics-informed neural networks for approximating solutions and boundaries.
result Successfully approximates solutions and moving boundaries in various Stefan problems.
GF-Net learns Green's functions for linear reaction-diffusion equations.
problem Learning Green's functions for linear reaction-diffusion equations on arbitrary domains.
method GF-Net, a neural network, learns Green's functions in an unsupervised manner using physics-informed approach and symmetry.
result GF-Net efficiently solves linear reaction-diffusion equations under various boundary conditions and sources.
This review discusses challenges and solutions for AI in chemical engineering.
problem Challenges in applying classical machine learning to chemical engineering data.
method Identifying four data characteristics and discussing their applications and solutions.
result Current research extends data science and machine learning to handle chemical engineering data challenges.
BoTorch optimizes Bayesian optimization with MC methods and auto-differentiation.
problem Efficient global optimization for various applications.
method Monte-Carlo acquisition functions, sample average approximation, auto-differentiation, variance reduction.
result Improved sample efficiency compared to other libraries.
DeepXDE uses neural networks to solve complex differential equations.
problem Solving differential equations using machine learning.
method Physics-informed neural networks (PINNs) with adaptive refinement.
result PINNs can solve various types of PDEs and inverse problems.
Soft-constrained PINN solves ODEs with minimal data, improving efficiency and robustness.
problem Sparse and noisy data in experiments and simulations.
method Soft-constrained Physics-informed Neural Network (PINN) with minimal labeled data.
result Soft-constrained PINN reduces need for labeled data and achieves strong generalization.
FD-Net predicts future dynamics from data using Hessian-Free TRCG method.
problem Discovering hidden partial differential equations from data.
method Finite-difference inspired convolutional neural network with Hessian-Free TRCG method.
result FD-Net predicts future dynamics efficiently using few trainable parameters.
Neural network learns fast PDE solvers with proven guarantees.
problem Designing fast iterative solvers for specific PDE problems.
method Learn to modify an existing solver using a deep neural network.
result Achieves 2-3 times speedup compared to state-of-the-art solvers.
Optimize black-box simulators with local generative models.
problem Optimizing non-differentiable, stochastic simulators with intractable likelihoods.
method Differentiable local surrogate models based on deep generative models.
result Local surrogates enable gradient-based optimization, faster than baseline methods.