Physics-informed machine learning: case studies for weather and climate modelling

Machine learning (ML) provides novel and powerful ways of accurately and efficiently recognizing complex patterns, emulating nonlinear dynamics, and predicting the spatio-temporal evolution of weather and climate processes. Off-the-shelf ML models, however, do not necessarily obey the fundamental governing laws of physical systems, nor do they generalize well to scenarios on which they have not been trained. We survey systematic approaches to incorporating physics and domain knowledge into ML models and distill these approaches into broad categories. Through 10 case studies, we show how these approaches have been used successfully for emulating, downscaling, and forecasting weather and climate processes. The accomplishments of these studies include greater physical consistency, reduced training time, improved data efficiency, and better generalization. Finally, we synthesize the lessons learned and identify scientific, diagnostic, computational, and resource challenges for developing truly robust and reliable physics-informed ML models for weather and climate processes. This article is part of the theme issue 'Machine learning for weather and climate modelling'.

Cranial vault expansion: a comparison of magnetic coupled distraction to traditional surgical repositioning

We compared the effectiveness of transcutaneously activated magnetic distraction of an osteotomized cranial bone flap to surgical repositioning of the flap with immediate, rigid internal fixation. Thirty immature rabbits were studied. All 30 rabbits underwent complete circumferential osteotomies of both parietal bones and postoperatively all were fitted with head frames. The rabbits were divided into 4 groups. The experimental magnetic distraction group consisted of 10 animals (group 1). In these rabbits magnets were secured to both parietal bones and magnets of opposite polarity were placed in the headframes. Each morning, the magnets in the head-frames were moved 0.25 mm farther away from the skull; this continued for 20 days for a total setback of 5 mm. Five animals served as the magnetic distraction controls; in these animals magnets were placed on the parietal bones but none were attached to the headframes (group 2). The experimental surgical repositioning group consisted of 10 rabbits (group 3). In each the parietal bones were elevated and fixed 5 mm above the rest of the skull using vitallium mesh and screws. Five rabbits made up the surgical respositioning control group (group 4). In these animals, parietal osteotomies were performed but the bones were secured to the skull in their original positions using hardware identical to that used in the experimental group. Six weeks later all of the animals were sacrificed. Two significant differences were identified between the experimental groups: (1) the cranial contours of the animals in the magnetic distraction group were rounded while those of the surgically repositioned group were acutely angled; (2) the osteotomies in rabbits in the magnetic distraction group were essentially completely ossified while in rabbits in the surgically repositioned group there were obvious gaps at the osteotomy sites that were filled with fibrous tissue. These conclusions support the potential utility of magnetically activated distraction as an alternative to current methods of cranial vault remodeling.

Development of a malignant peripheral nerve sheath tumor following treatment for testicular seminoma

A novel case is reported in which an S2 nerve root malignant peripheral nerve sheath tumor was diagnosed approximately 8 years after treatment for Stage I testicular seminoma. This patient underwent right orchiectomy and subsequent irradiation therapy to the periaortic region, including the sacrum. Postoperative radiation therapy likely played a role in the development of this second malignancy.

Primary Ki-1 (anaplastic large cell) lymphoma of the brain and spinal cord

The authors report a case of primary Ki-1 lymphoma of the brain. The patient was a 4 1/2-year-old black girl who presented with a 4- and 5-day history of headaches, nausea, vomiting, neck stiffness, and difficulty in walking. Computed tomography (CT) scan of the brain showed two discrete densities in the left occipital lobe and in the brain stem. Magnetic resonance imaging (MRI) showed multiple densities scattered over the brain surface and brain stem. Microscopically, the tumor was an anaplastic neoplasm that diffusely infiltrated brain parenchyma. The neoplastic cells were large with amphophilic cytoplasm, large nuclei with irregular nuclear contours and prominent nucleoli. A high mitotic rate including atypical mitotic figures was noted. Immunohistochemical stains showed diffuse strong positivity for CD30 and moderate focal staining for epithelial membrane antigen. Leukocyte common antigen, cytokeratin, neuron specific enolase, monocyte/macrophage and B- and T-marker stains were negative. The histology was characteristic for Ki-1 large cell lymphoma. Cytologic examination of cerebrospinal fluid (CSF) demonstrated similar neoplastic cells. This is one of the first reports of this variant in the pediatric population.

Hyperdense basilar artery. An early computed tomography sign of thrombosis

Noncontrast computed tomographic scans (CT scans) may show a hyperdense basilar artery before a brainstem infarct is visualized. This early sign should assist clinicians in confirming the diagnosis of basilar artery thrombosis. In a review of admission records of 750 patients with acute cerebrovascular disease from July 1991 to June 1993, at Saint Louis University Hospital, 20 patients were identified with clinical signs of nonlacunar, vertebrobasilar distribution infarction. Eight of these had pontomesencephalic ischemia. Their neuroimaging studies and medical records were evaluated. Four patients with acute clinical signs of pontomesencephalic infarction were found to have a hyperdense basilar artery on CT scans. The scans of 2 patients were excluded because of dolichoectasia; in the other 2 patients, the basilar artery appeared normal on the CT scan. The hyperdense basilar artery was detected within the early hours of neurological symptoms and often was the only detectable abnormality on the scan. In 3 patients extensive brainstem infarcts subsequently developed and they died. Basilar artery thrombosis was confirmed by pathological study in all these patients. In the fourth patient basilar artery occlusion and a large pontine infarct were evident by magnetic resonance imaging and angiography. A hyperdense basilar artery is a common feature on CT scans of patients presenting with an early clinical diagnosis of thrombosis. Untreated, the hyperintense basilar artery often portends a poor prognosis. Its ready recognition should guide further interventional studies and treatment.

Recurrent syncope and quadriplegia

A 72-year-old man had posturally induced syncopal episodes, followed by quadriparesis, coma, and death. Neuroimaging studies supported the clinical diagnosis confirmed by neuropathological findings.

Unusual hemorrhage with use of synthetic dural substitute: MR findings

Delayed hemorrhage is an unusual complication of silastic dural substitute that can have a prolonged latent period. Two such patients that presented 6 and 12 years following surgery and that were evaluated by MR imaging are reported.