BENO: Boundary-embedded Neural Operators for Elliptic PDEs

Elliptic partial differential equations (PDEs) are a major class of time-independent PDEs that play a key role in many scientific and engineering domains such as fluid dynamics, plasma physics, and solid mechanics. Recently, neural operators have emerged as a promising technique to solve elliptic PDEs more efficiently by directly mapping the input to solutions. However, existing networks typically cannot handle complex geometries and inhomogeneous boundary values present in the real world. Here we introduce Boundary-Embedded Neural Operators (BENO), a novel neural operator architecture that embeds the complex geometries and inhomogeneous boundary values into the solving of elliptic PDEs. Inspired by classical Green's function, BENO consists of two branches of Graph Neural Networks (GNNs) for interior source term and boundary values, respectively. Furthermore, a Transformer encoder maps the global boundary geometry into a latent vector which influences each message passing layer of the GNNs. We test our model extensively in elliptic PDEs with various boundary conditions. We show that all existing baseline methods fail to learn the solution operator. In contrast, our model, endowed with boundary-embedded architecture, outperforms state-of-the-art neural operators and strong baselines by an average of 60.96\%. Our source code can be found https://github.com/AI4Science-WestlakeU/beno.git.Comment: Accepted by ICLR 202

Temperature mapping using photoacoustic and thermoacoustic tomography

Photoacoustic (PA) and thermoacoustic (TA) effects are based on the generation of acoustic waves after tissues absorb electromagnetic energy. The amplitude of the acoustic signal is related to the temperature of the absorbing target tissue. A combined photoacoustic and thermoacoustic imaging system built around a modified commercial ultrasound scanner was used to obtain an image of the target's temperature, using reconstructed photoacoustic or thermoacoustic images. To demonstrate these techniques, we used photoacoustic imaging to monitor the temperature changes of methylene blue solution buried at a depth of 1.5 cm in chicken breast tissue from 12 to 42 °C. We also used thermoacoustic imaging to monitor the temperature changes of porcine muscle embedded in 2 cm porcine fat from 14 to 28 °C. The results demonstrate that these techniques can provide noninvasive real-time temperature monitoring of embedded objects and tissue

Performance characterization of an integrated ultrasound, photoacoustic, and thermoacoustic imaging system

We developed a novel trimodality system for human breast imaging by integrating photoacoustic (PA) and thermoacoustic (TA) imaging techniques into a modified commercial ultrasound scanner. Because light was delivered with an optical assembly placed within the microwave antenna, no mechanical switching between the microwave and laser sources was needed. Laser and microwave excitation pulses were interleaved to enable PA and TA data acquisition in parallel at a rate of 10 frames per second. A tube (7 mm inner diameter) filled with oxygenated bovine blood or 30 mM methylene blue dye was successfully detected in PA images in chicken breast tissue at depths of 6.6 and 8.4 cm, respectively, for the first time. The SNRs at these depths reached ∼24 and ∼15  dB, respectively, by averaging 200 signal acquisitions. Similarly, a tube (13 mm inner diameter) filled with saline solution (0.9%) at a depth of 4.4 cm in porcine fat tissue was successfully detected in TA images. The PA axial, lateral, and elevational resolutions were 640 μm, 720 μm, and 3.5 mm, respectively, suitable for breast cancer imaging. A PA noise-equivalent sensitivity to methylene blue solution of 260 nM was achieved in chicken tissue at a depth of 3.4 cm

Single-cell photoacoustic thermometry

A novel photoacoustic thermometric method is presented for simultaneously imaging cells and sensing their temperature. With three-seconds-per-frame imaging speed, a temperature resolution of 0.2°C was achieved in a photo-thermal cell heating experiment. Compared to other approaches, the photoacoustic thermometric method has the advantage of not requiring custom-developed temperature-sensitive biosensors. This feature should facilitate the conversion of single-cell thermometry into a routine lab tool and make it accessible to a much broader biological research community

Efficient Formulation of Polarizable Gaussian Multipole Electrostatics for Biomolecular Simulations

Molecular dynamics simulations of biomolecules have been widely adopted in biomedical studies. As classical point-charge models continue to be used in routine biomolecular applications, there have been growing demands on developing polarizable force fields for handling more complicated biomolecular processes. Here we focus on a recently proposed polarizable Gaussian Multipole (pGM) model for biomolecular simulations. A key benefit of pGM is its screening of all short-range electrostatic interactions in a physically consistent manner, which is critical for stable charge-fitting and is needed to reproduce molecular anisotropy. Another advantage of pGM is that each atom's multipoles are represented by a single Gaussian function or its derivatives, allowing for more efficient electrostatics than other Gaussian-based models. In this study we present an efficient formulation for the pGM model defined with respect to a local frame formed with a set of covalent basis vectors. The covalent basis vectors are chosen to be along each atom's covalent bonding directions. The new local frame allows molecular flexibility during molecular simulations and facilitates an efficient formulation of analytical electrostatic forces without explicit torque computation. Subsequent numerical tests show that analytical atomic forces agree excellently with numerical finite-difference forces for the tested system. Finally, the new pGM electrostatics algorithm is interfaced with the PME implementation in Amber for molecular simulations under the periodic boundary conditions. To validate the overall pGM/PME electrostatics, we conducted an NVE simulation for a small water box of 512 water molecules. Our results show that, to achieve energy conservation in the polarizable model, it is important to ensure enough accuracy on both PME and induction iteration

Evaluating the effect of curing conditions on the glass transition of the structural adhesive using conditional tabular generative adversarial networks

Owing to its structural advantages, adhesively bonding fibre-reinforced polymers have been a promising solution for strengthening constructions. However, the effectiveness of this technique is significantly influenced by the material properties of the adhesive layer, which are largely determined by its curing condition. A comprehensive analysis of the effect of curing conditions on structural adhesives is hampered by the lack of sufficient experimental data. To mitigate such a limitation, this present study utilises a deep machine learning (ML) tool, the conditional tabular generative adversarial networks (CTGAN), to generate plausible synthetic dataset for developing a robust data-driven model. An artificial neural network (ANN) was trained on synthetic data and tested on real data, following the "Train on Synthetic – Test on Real" philosophy. The ultimately developed CTGAN-ANN model was validated by newly conducted experiments and several published studies (R2 ≥ 0.95), which demonstrated the ability to provide accurate estimates of the glass transition temperature values of the polymer adhesive. A comprehensive evaluation of the effect of each curing condition variable on the adhesive was performed, which revealed the underlying relationships, indicating that curing temperature and curing time have a positive effect, but that curing humidity has a negative effect. The ML model developed could inform the practical use of the structural adhesive in civil engineering